Question

A car starts from rest and acceleration at $4{m/s}^2$ for $5s$. After that it moves with constant velocity for $25s$ and then retards at $2m/s^2$ until it comes to rest. The total distance travelled by the car is

• A. $650m$
• B. $527m$
• C. $675m$
• D. $573m$

Answer 1

The correct option is A $650m$

For $0-5sec$,

$a=4m/s^2$, Let velocity at $5sec$ is $v$ and distance is $S_1$

Using $v=u+at$ $\Rightarrow v=0+4\times 5=20m/s$

Using $s=ut+\frac{1}{2}a{t}^2$ $\Rightarrow S_1=0+\frac{1}{2}\times 4\times 5^2=50m$

For next $25sec$

$v=20m/s$

$\Rightarrow S_2=20\times 25=500m$

For comes to rest,

$u=20m/s$ , $a=-2m/s^2$

Using $v^2=u^2+2as$ $\Rightarrow 0={20}^2-2\times 2\times S_3$

$\Rightarrow S_3=100m$

Total distance $=S_1+S_2+S_3=50+500+100=650m$