Question

The initial velocity of a particle is $u$(at $t=0$) and the acceleration a is given by $\alpha t^{3/2}$. Which of the following relations is valid?

• A. $v=u+\alpha t^{3/2}$
• B. $v=u+\frac{3\alpha t^3}{2}$
• C. $v=u+\frac{2}{5}\alpha t^{5/2}$
• D. $v=u+\alpha t^{5/2}$

Answer 1

The correct option is C $v=u+\frac{2}{5}\alpha t^{5/2}$

Given initial velocity =$u$, acceleration $=\alpha t^{3/2}$

Also we know $\frac{du}{dt}=a$

$du=adt$

Now integrating the above equation we get,

${\int }_u^{v}du=\alpha {\int }_0^t{t}^{\frac{3}{2}}dtv-u=\frac{2}{5}\alpha t^{\frac{5}{2}}v=u+\frac{2}{5}\alpha t^{\frac{5}{2}}$