Question

A car starts from rest and moves with a constant acceleration of $5m/s^2$ for $10s$ before the driver applies the brake. It then decelerates for $5s$ before coming to rest, then the average speed of the car over the entire journey of the car is

• A. 23 m / s
• B. 30 m / s
• C. 33 m / s
• D. 25 m / s

Answer 1

Answer: (D)

Schematic diagram for motion of body is

Average speed $=\frac{\text{ Total displacement }}{\text{ Total time }}$
In interval $t=0$ to $t=10s$;
Displacement, $s_1=\frac{1}{2}{a}_1{t}^2=\frac{1}{2}\times 5\times (10{)}^2=250m$
Final velocity, $v_1=u+a_{1}t$
$\Rightarrow v_1=0+5\times 10=50m{s}^{-1}$
In interval $t=10s$ to $t=15s$,
$v_1=50m{s}^{-1},v_2=0m{s}^{-1},t=5s$
Using $v=u+at$
We have, $a_2=\frac{0-50}{5}=-10m{s}^{-2}$
And by $v^2-u^2=2as$, we have
$v_2^2-v_1^2=2\left(a_2\right)s_2$
$\Rightarrow s_2=\frac{50\times 50}{2\times 10}=125m$
So, average speed for interval, $t=0$ to $t=15s$,
We have
$v_{\text{avg }}=\frac{s_1+s_2}{t_1+t_2}=\frac{250+125}{10+5}=\frac{375}{15}$
$=25m{s}^{-1}$