
If the velocity \[\upsilon \] of a particle moving along a straight line decreases linearly with its displacement S is \[20\,\,m{{s}^{1}}\] to a value approaching to zero at \[S=30\,m,\] then acceleration of the particle at \[S=15\text{ }m,\] is
A)
\[\frac{2}{3}m{{s}^{2}}\] done
clear
B)
\[\frac{2}{3}m{{s}^{2}}\] done
clear
C)
\[\frac{20}{3}m{{s}^{2}}\] done
clear
D)
\[\frac{20}{3}m{{s}^{2}}\] done
clear
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A body is thrown vertically upward in air when air resistance is taken into account, the time of ascent is \[{{t}_{1}}\] and time of descent is \[{{t}_{2}}\], then which of the following is true?
A)
\[{{t}_{1}}={{t}_{2}}\] done
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B)
\[{{t}_{1}}<{{t}_{2}}\] done
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C)
\[{{t}_{1}}>{{t}_{2}}\] done
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D)
\[{{t}_{1}}\ge \,\,{{t}_{2}}\] done
clear
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A point moves with uniform acceleration and \[{{v}_{1}},\text{ }{{v}_{2}},\text{ }{{v}_{3}}\] denote the average velocities in three successive intervals of time \[{{t}_{1}},\text{ }{{t}_{2}},\text{ }{{t}_{3}}\]. Which of the following relations is correct?
A)
\[({{v}_{1}}{{v}_{2}}):({{v}_{2}}{{v}_{3}})=({{t}_{1}}{{t}_{2}}):\text{(}{{t}_{2}}+{{t}_{3}})\] done
clear
B)
\[({{v}_{1}}{{v}_{2}}):({{v}_{2}}{{v}_{3}})=({{t}_{1}}+{{t}_{2}}):\text{(}{{t}_{2}}+{{t}_{3}})\] done
clear
C)
\[({{v}_{1}}{{v}_{2}}):({{v}_{2}}{{v}_{2}})=({{t}_{1}}{{t}_{2}}):\text{(}{{t}_{2}}{{t}_{3}})\] done
clear
D)
\[({{v}_{1}}{{v}_{2}}):({{v}_{2}}+{{v}_{3}})=({{t}_{1}}{{t}_{2}}):\text{(}{{t}_{2}}+{{t}_{3}})\] done
clear
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A boy sitting on the top most berth in the compartment of a train which is just going to stop on a railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about 2 m. The apple will fall
A)
precisely in the hand of his brother done
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B)
slightly away from the hand of his brother in the direction of motion of the train done
clear
C)
slightly away from the hand of his brother in the direction opposite to the direction of motion of the train done
clear
D)
None of the above done
clear
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The velocitytime graph of a body is shown in figure. It implies that at point B.
A)
the force is zero done
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B)
there is a force towards motion done
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C)
there is a force which opposes motion done
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D)
there is only gravitational force done
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A juggler throws balls into air. He throws one whenever previous one is at its highest point, if he throws n balls per second, then the height to which each ball will rise is
A)
\[g/n\] done
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B)
\[g/{{n}^{2}}\] done
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C)
\[g/2{{n}^{2}}\] done
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D)
\[g/4{{n}^{2}}\] done
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The displacement \[\times \] of a particle is given by \[x=a{{e}^{\alpha t}}+b{{e}^{\beta t}}\] with \[a,\,b,\,\alpha \] and \[\beta \] as constants. With increase in time, the associated velocity
A)
increases done
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B)
decreases done
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C)
increases and decreases done
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D)
decreases and increases done
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A wooden block is dropped from the top of a cliff 100 m high. Simultaneously a bullet is fired from the foot of the cliff upward with a velocity of 100 m/s. The bullet hits the wooden block after  \[[Takeg=10\text{ }m/{{s}^{2}}]\]
A)
10 s done
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B)
0.5 s done
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C)
1 s done
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D)
7 s done
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A bus is beginning to move with an acceleration of \[1\text{ }m{{s}^{2}}\]. A boy who is 48 m behind the bus starts running at \[10\text{ }m{{s}^{1}}\]. After what time will the boy be able to catch the bus?
A)
6 s done
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B)
8 s done
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C)
10 s done
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D)
The boy cannot catch the bus done
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A train is moving along a straight path with uniform acceleration. Its engine passes across a pole with a velocity of \[60\text{ }km{{h}^{1}}\] and the end (guard's van) passes across same pole with a velocity of \[60\text{ }km{{h}^{1}}\]. The middle point of the train will pass across same pole with a velocity
A)
\[70\text{ }km{{h}^{1}}\] done
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B)
\[70.7\text{ }km{{h}^{1}}\] done
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C)
\[65\text{ }km{{h}^{1}}\] done
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D)
\[75\text{ }km{{h}^{1}}\] done
clear
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A point moves in a straight line so that its displacement x metre at time t second is given by \[{{x}^{2}}=1+{{t}^{2}}\]. Its acceleration in \[m{{s}^{2}}\] at time second is
A)
\[\frac{1}{{{x}^{3}}}\] done
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B)
\[\frac{1}{x}\,\frac{1}{{{x}^{2}}}\] done
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C)
\[\frac{t}{{{x}^{2}}}\] done
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D)
\[\frac{1}{x}\,\,\frac{{{t}^{2}}}{{{x}^{3}}}\] done
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A body starts with some initial velocity and a constant acceleration. It covers a distance of 200 m in first four second and a distance of 220 m in next two second. The acceleration of the body and its velocity at the end of seventh second are
A)
\[a=5\,m{{s}^{2}},\,\,\upsilon =75\,m{{s}^{1}}\] done
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B)
\[a=7.5\,m{{s}^{2}},\,\upsilon =100\,m{{s}^{1}}\] done
clear
C)
\[a=20\,m{{s}^{2}},\,\upsilon =150\,m{{s}^{1}}\] done
clear
D)
\[a=150\,m{{s}^{2}},\,\upsilon =10\,m{{s}^{1}}\] done
clear
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If a car covers 2/5th of the total distance with \[{{v}_{1}}\] speed and 3/5th distance with \[{{v}_{2}},\] then average speed is
A)
\[\frac{1}{2}\,\sqrt{{{v}_{1}}{{v}_{2}}}\] done
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B)
\[\frac{{{v}_{1}}+{{v}_{2}}}{2}\] done
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C)
\[\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\] done
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D)
\[\frac{5{{v}_{1}}{{v}_{2}}}{3{{v}_{1}}+2{{v}_{2}}}\] done
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A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after \[{{t}_{1}}\] and \[{{t}_{2}}\] seconds, respectively, then
A)
\[t={{t}_{1}}{{t}_{2}}\] done
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B)
\[t=\frac{{{t}_{1}}+{{t}_{2}}}{2}\] done
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C)
\[t=\sqrt{{{t}_{1}}{{t}_{2}}}\] done
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D)
\[t_{1}^{2}=t_{2}^{2}\] done
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A body starts from rest with uniform acceleration. If its velocity after n second is l), then its displacement in the last two seconds is
A)
\[\frac{2\upsilon (n+1)}{n}\] done
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B)
\[\frac{\upsilon (n+1)}{n}\] done
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C)
\[\frac{\upsilon (n1)}{n}\] done
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D)
\[\frac{2\upsilon (n1)}{n}\] done
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A particle is moving rectilinearly with acceleration a, whose value is given as a function of distance by the equation \[a=\alpha \sqrt{x},\] find displacement as a function of time. [At \[t=0,\] particle is at rest at \[x=0\]]
A)
\[\frac{4a{{t}^{3}}}{2}\] done
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B)
\[\left( \frac{\sqrt{\alpha }}{6} \right)t\] done
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C)
\[\left( \frac{{{\alpha }^{2}}}{36} \right){{t}^{4}}\] done
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D)
\[\left( \frac{{{\alpha }^{2}}}{144} \right){{t}^{4}}\] done
clear
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Direction: A particle initially (i.e., at time \[t=0\]) moving with a velocity u subjected to a retarding force, as a result of which it decelerates at a rate \[a=k\,\sqrt{v}\] where v is the instantaneous velocity and k is a positive constant. 
The particle comes to rest in a time 
A)
\[\frac{2\sqrt{u}}{k}\] done
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B)
\[\frac{\sqrt{u}}{k}\] done
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C)
\[2k\sqrt{u}\] done
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D)
\[k\sqrt{u}\] done
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Direction: A particle initially (i.e., at time \[t=0\]) moving with a velocity u subjected to a retarding force, as a result of which it decelerates at a rate \[a=k\,\sqrt{v}\] where v is the instantaneous velocity and k is a positive constant. 
The distance covered by the particle before coming to rest is 
A)
\[\frac{{{u}^{3/2}}}{k}\] done
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B)
\[\frac{2{{u}^{3/2}}}{k}\] done
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C)
\[\frac{3{{u}^{3/2}}}{2k}\] done
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D)
\[\frac{2{{u}^{3/2}}}{3k}\] done
clear
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A body covered a distance of L m along a curved path of a quarter circle. The ratio of distance to displacements
A)
\[\frac{\pi }{2\sqrt{2}}\] done
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B)
\[\frac{2\sqrt{2}}{\pi }\] done
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C)
\[\frac{\pi }{\sqrt{2}}\] done
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D)
\[\frac{\sqrt{2}}{\pi }\] done
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A particle is resting over a smooth horizontal floor. At \[t=0\] a horizontal force starts acting on it. Magnitude of the force increases with time according to law \[G=\alpha t,\] where a is a positive constant and t is time. For the figure shown which of the following statements is/are incorrect?
A)
Curve 1 shows acceleration against time done
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B)
Curve 2 shows velocity against time done
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C)
Curve 2 shows velocity against acceleration done
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D)
none of these done
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The velocity v and position r of a body are related as, \[{{v}^{2}}=kr,\] where k is a constant. What will be the velocity after 1 second? Given that the position is zero at \[t=0\].
A)
\[\sqrt{kr}\] done
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B)
\[k{{r}^{3/2}}\] done
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C)
\[\frac{k}{2}{{r}^{0}}\] done
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D)
cannot be determined from the given information done
clear
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Two balls of equal masses are thrown upwards, along the same vertical direction at an interval of 2 seconds, with the same initial velocity of 40 m/s. Then these collide at a height of (Take \[g=10\,m/{{s}^{2}}\])
A)
120 m done
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B)
75 m done
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C)
200 m done
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D)
45 m done
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A person climbs up a stalled escalator in 60 sec. When he stands on it then he is carried in the moving escalator in 30 sec. How much time will he take in climbing up in a moving escalator?
A)
10 sec done
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B)
30 sec done
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C)
20 sec done
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D)
40 sec done
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The position of a particle vary \[x=4t2{{t}^{2}}\]. The distance covered by particle in 4 s is
A)
5 m done
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B)
1 m done
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C)
2 m done
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D)
4 m done
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A body moves in a straight line along xaxis. Its distance from the origin is given by\[x=9t3{{t}^{2}}\]. The average velocity between \[t=0\] to \[t=4\] is
A)
\[3\,m{{s}^{1}}\] done
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B)
\[4\,m{{s}^{1}}\] done
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C)
\[16\,m{{s}^{1}}\] done
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D)
\[12\,m{{s}^{1}}\] done
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Balls are dropped from the roof of a tower at a fixed interval of time. At the time when 9th ball reaches the ground, nth ball is at 3/4th height of the tower. The value of n is
A)
3 done
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B)
7 done
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C)
6 done
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D)
5 done
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A rifle bullet loses \[\frac{1}{4}\] of its velocity in passing through a wooden plank. The least number of planks required to stop the bullet is (assume uniform retardation in the plank)
A)
4 done
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B)
5 done
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C)
2 done
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D)
3 done
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A body starts from rest with uniform acceleration a, its velocity after n seconds is \[\upsilon \]. The displacement of the body in last 3 seconds is:
A)
\[\frac{\upsilon (6n9)}{2n}\] done
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B)
\[\frac{2\upsilon (6n9)}{n}\] done
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C)
\[\frac{2\upsilon (2n+1)}{n}\] done
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D)
\[\frac{2\upsilon (n1)}{n}\] done
clear
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Two buses moving in opposite directions with velocities of 16 m/s and 12 m/s have lengths of 6 m and 8 m respectively. The minimum road length required for overtaking is
A)
14 m done
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B)
28 m done
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C)
22 m done
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D)
20 m done
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A force F acts on a body of mass 1 kg moving in a straight line with an initial velocity u for 1s, then
A)
distance covered by the body is \[u+F/2\] done
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B)
momentum of the body increases by F done
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C)
final velocity of the body is \[u\text{ }+\text{ }F\] done
clear
D)
all of these done
clear
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The engine of a motor cycle can produce maximum acceleration \[5\text{ }m/se{{c}^{2}}\]. Its breaks can produce a maximum retardation \[10\text{ }m/se{{c}^{2}}\]. What is minimum time in which it can cover a distance of 1.5 km:
A)
5 sec. done
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B)
10 sec. done
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C)
15 sec. done
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D)
30 sec. done
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A body moves with uniformly accelerated motion and travels 200 cm in the first two seconds and 220 cm in the next four seconds. What will be the velocity at the end of 7 seconds from start?
A)
 10 cm/s done
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B)
10 cm/s done
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C)
20 cm/s done
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D)
30 cm/s done
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A point mass starts moving in straight line with constant acceleration a from rest at \[t=0.\] At time \[t=2s\], the acceleration changes the sign, remaining the same in magnitude. The mass returns to the initial position at time \[t={{t}_{0}}\] after start of motion. Here \[{{t}_{0}}\] is:
A)
4s done
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B)
\[(4+2\sqrt{2})s\] done
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C)
\[(2+2\sqrt{2})s\] done
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D)
\[(4+4\sqrt{2})s\] done
clear
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A cyclist starts from the centre O of a circular track of radius R = 2 km, moves along radius OP and then moves from P to Q along the circumference and there at Q it stops. The total time of motion of the cyclist is 45 min. The average speed of the cyclist is
A)
8 km/h done
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B)
6.86 km/h done
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C)
15.23 km/h done
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D)
None of these done
clear
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Acceleration versus velocity graph of a particle moving in a straight line is as shown in figure. The corresponding velocitytime graph would be
A)
B)
C)
D)
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