Question

A particle starts from rest. Its acceleration at time t = 0 is 5 $m{s}^{-2}$ Which varies with time as shown in fig. The maximum speed of the particle will be

• A. $7.5m{s}^{-1}$
• B. $15m{s}^{-1}$
• C. $30m{s}^{-1}$
• D. $75m{s}^{-1}$

Answer 1

Answer: (B)

$15m{s}^{-1}$

The acceleration becomes $zero$ at the end of $t=6s$

so the velocity will $stop$ from $increasing$ so the velocity will be maximum at the end of $t=6s$

now as the velocity in start of the motion was $zero$ so the velocity after $t=6s$ will be just the $increase$ in velocity by

acceleration in these $6s$ which is given by the $area$ under the a-t $graph$

the area is $\frac{1}{2}\times base\times height=\frac{1}{2}\times 6s\times 5m/s^2=15m/s$

so maximum velocity is $15m/s$