Question

A body is started from rest with acceleration $2m/s^2$ till it attains the maximum velocity then retard to rest with $3m/s^2$. If total time taken is 10 second then maximum speed attained is

• A. 12 m/s
• B. 8 m/s
• C. 6 m/s
• D. 4 m/s

Answer 1

Answer: (A)

12 m/s

Given that,

Acceleration $a=2m/s^2$

Retardation $a=-3m/s^2$

Time $t=10s$

Now, from equation of motion

The maximum velocity attained be v at t

$v=u+at$

$v=0+2\times t$

$v=2tm/s.....\left(I\right)$

Now, again it reaches velocity 0 after 10 s with retardation

$v=u+at$

$0=v-3(10-t)$

Now from equation (I)

$2t-3(10-t)=0$

$2t-30+3t=0$

$5t=30$

$t=6s$

Now, put the value of t in equation (I)

$v=2t$

$v=2\times 6$

$v=12m/s$

Hence, the maximum speed is $12m/s$