Answer:
Initial velocity of a car\[=u=36\,km/hr=\]
\[36\times \frac{1000}{3600}m/s=10m/s\]
Final velocity of a car\[=v=0\,m/s\]
The car stops at a distance = s
\[=51\,m-1\,m=50\,m\]
Total weight of the car and the passenger
= 2000 kg
Retarding force\[=F=?\]
Time required to stop the car\[=t=?\]
We know that F = ma
How to find a in terms of the given data u, v, a and t ?
We know that \[{{v}^{2}}-{{u}^{2}}=2as\] ……(1)
Substituting the above values in (1), we get
\[{{(0)}^{2}}-{{(10)}^{2}}=2\times a\times 50\Rightarrow -100=100\times a\]c
\[\Rightarrow a=\frac{-100}{100}=-1m/{{s}^{2}}\] ….… (2)
\[\therefore \]Retarding force \[=F=ma\] …… (3)
Substituting value of ‘m’ and ‘a’ in (3), we get
\[F=(2000\times -1)kgm/{{s}^{2}}\Rightarrow F=-2000N\]
Also we know that,
\[a=\frac{v-a}{t}\Rightarrow t=\frac{v-u}{a}\] …. (4)
Again, substituting the above values in (4), we get
\[t=\frac{(0-10)}{-1}=\frac{-10}{-1}\sec =10\sec \]
Therefore, time required to stop the car is 10 sec.
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