| (i) \[100\,m{{s}^{-1}}\] |
| (ii)\[136\,km\,\,{{h}^{-1}}\] |
| (iii)\[1000\,cm\,\,{{s}^{-1}}\] |
| (iv) \[600\,m\,\,{{\min }^{-1}}\] |
A) Only (i) and (ii)
B) Only (ii) and (iii)
C) Only (i), (iii) and (iv)
D) Only (ii), (iii) and (iv)
Correct Answer: D
Solution :
Speed with which a car covers a distance of 3 km in 5 minutes can be\[36\text{ }km\text{ }{{h}^{-1}},\] or \[\text{1000 c}m\text{ }{{\text{s}}^{-1}}\] or \[600\,m\,{{(min)}^{-1}}\] or \[10\,m\,{{s}^{-1}}.\] (i) \[\text{Speed}\,\text{(in}\,\text{km/h)=}\frac{\text{Distance}\,\text{in}\,\text{km}}{\text{Time}\,\text{in}\,\text{hour}}\] Distance = 3 km Time (in min) = 5 minutes \[\therefore \]Time (in hours) \[=\frac{1}{60}\times 5=\frac{1}{12}\,hr\] \[\therefore \]\[Speed=3\times 12=36\text{ }k\,m\,{{h}^{-1}}\] (ii) \[\text{Speed}\,\text{in}\,\text{(cm/s)=}\frac{\text{Distance}\,\text{in}\,\text{cm}}{\text{Time}\,\text{in}\,\text{second}}\] Distance = 3 km Distance (in cm) = 10, 0000 cm \[\times \] 3 = 30, 0000 cm \[\therefore \]\[Speed=\frac{30,0000}{300}=1000\,cm\,{{s}^{-1}}\] (iii) \[\text{Speed in m/min}\,\text{=}\,\frac{\text{Distance}\,\text{in}\,\text{metres}}{\text{Time}\,\text{in}\,\text{minutes}}\] Distance = 3000 m Time = 5 minutes \[\therefore \] \[Speed=\frac{3000}{5}=600\,m\,{{\min }^{-1}}\]
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