Question

A car starts from rest and accelerates at uniform rate of $5m/s^2$ for some time, then moves with contant speed for some time and retards at the same uniform rate and comes to rest. Total time for the journey is 25 sec and average speed for the journey is 20 m/s. How long does the car move with constant speed?

• A. 10 sec
• B. 12 sec
• C. 15 sec
• D. 18 sec

Answer 1

The correct option is C 15 sec

Avg speed $\times$ total times = total distance
$20\times 25=500$
Since acceleration in the 1st interval is same as deceleration in the 3rd interval and deceleration is from the same velocity achieved after acceleration, $t_1=t_3$
$s_1=\frac{1}{2}\times 5t_1^2$
$s_2=\left(5t_1\right)t_2$
$s_3=\left(5t_1\right)\times t_3-\frac{1}{2}\times 5\times t_1^2=\left(5t_1\right)\times t_1-\frac{1}{2}\times 5\times t_1^2$
$s_1+s_2+s_3=5t_1{t}_2+5t_1^2$
$\Rightarrow 5t_1^2+5t_1{t}_2=500----1$
$2t_1+t_2=25----2$
Solving (1 ) and (2) $\Rightarrow t_1=5,t_2=15sec$