Question

Acceleration of a particle starting from rest varies with time $(t)$ according to relation $a=\alpha t+\beta$ $(\alpha$ and $\beta$ are positive constant). The velocity $v$ of particle as a function of time is given as.

• A. $v=\frac{\alpha t^2+\beta }{2}$
• B. $v=\alpha t^2+\beta t$
• C. $v=\frac{\alpha t^2}{2}+\beta t$
• D. $v=\alpha t^2+2\beta t$

Answer 1

Answer: (C)

Since acceleration is variable so to find $v$ we use integration
$v=\int adt$
$v=\underset{0}{\overset{t}{\int }}(\alpha t+\beta )dt$
$u=0$
$=\alpha {\left[\frac{t^2}{2}\right]}_0^t+[\beta t{]}_0^t$
$=\frac{\alpha t^2}{2}+\beta t$