Question

A bus starts from rest with $2m{s}^{-2}$ for 10 seconds and then returned with $4m{s}^{-2}$ and finally comes to rest the total distance travelled by bus is.

• A. $100m$
• B. $50m$
• C. $150m$
• D. $200m$

Answer 1

The correct option is C $150m$

Given,

Initial velocity is zero, $u=0$, accelerated by $a_1=2m{s}^{-1}$ and time $t=10\sec$

$v=u+at$

$v_1=0+2\times 10\Rightarrow v_1=20m{s}^{-1}$

In the second event, final velocity $v_3=0$, retarded by $a_2=-4m{s}^{-2}$

$0=v_1-4t_2$

$t_2=\frac{v_1}{4}=\frac{20}{4}=5\sec$

Displacement, $s=ut+\frac{1}{2}a{t}^2$

$s_1=u{t}_1+\frac{1}{2}{a}_1{t_1}^2=0+\frac{1}{2}2\times {10}^2=100m$

$s_2=v_1{t}_2+\frac{1}{2}{a}_2{t_2}^2=20\times 5+\frac{1}{2}(-4)\times 5^2=50m$

Total displacement, $s_1+s_2=100+50=150m$

Total displacement is $150m$