Question

The acceleration time graph of the motion of a particle from $A$ to $B$ is semicircle with radius of $\sqrt{(}7)$ unit. Find the velocity of particle at $t_2$ if at $t_1$, velocity is $3m/sec.[\pi =\frac{22}{7}]$

• A. $\frac{17}{2}m/sec$
• B. $8m/sec$
• C. $\frac{15}{2}m/sec$
• D. None of these

Answer 1

The correct option is A $\frac{17}{2}m/sec$

$\left(A\right)$

Area under $acceleration-timegraph=changeinvelocity$

$a=\frac{dv}{dt}$

$dv=adt$

$v_{t_2}-v_{t_1}={\int }_{t_1}^{t_2}adt$

$v_{t_2}-3=\frac{\pi r^2}{4}$

$v_{t_2}=3+\frac{7\pi }{4}$

$v_{t_2}=3+\frac{22}{4}$

$v_{t_2}=\frac{17}{2}m/s$