Q. A body moves for a total of nine second starting from rest with uniform acceleration and then with uniform retardation, which is twice the value of acceleration and then stops. The duration of uniform acceleration
A) $3\ s$
B) $4.5\ s$
C) $5\ s$
D) $6\ s$
Explanation
(d) Let acceleration is $a$ and retardation is $- 2a$
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Then for acceleration motion
$t_{1} = \frac{v}{a}$ …(i)
For retarding motion
$t_{2} = \frac{v}{2a}$ …(ii)
Given $t_{1} + t_{2} = 9 \Rightarrow \frac{v}{a} + \frac{v}{2a} = 9 \Rightarrow \frac{3v}{2a} = 9 \Rightarrow \frac{v}{a} = 6$
Hence, duration of acceleration, $t_{1} = \frac{v}{a} = 6\ sec$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.