Question

A car starts accelerating in a straight line path from rest with $5m{s}^{-2}$ for sometime, then uniformly and finally decelerates at $5m{s}^{-2}$ and comes to a stop. The total time of motion equals $25s$. How long does the car move uniformly? Given average velocity is $V_{av}=72km/h$ during motion.

• A. $5s$
• B. $10s$
• C. $15s$
• D. $20s$

Answer 1

Answer: (C)

$15s$

by the given graph we would find,

total distance covered=area under $V-t$ curve.

$20\times 25=2\times (\frac{1}{2}\times 5{t_1}^2)+(25-2t_1)5t_1$

Solving the quadratic equation, we get $t_1=5,20$
20 is not possible since $25-2t_1$ has to be positive.
Putting $t_1=5$, we get $25-2t_1=15$

so car will move uniformly for 15 seconds.