Question

The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from origin with an initial velocity $v_0$. The distance travelled by the particle in time $t$ will be

• A. $v_{0}t+\frac{1}{6}b{t}^3$
• B. $v_{0}t+\frac{1}{2}b{t}^2$
• C. $v_{0}t+\frac{1}{3}b{t}^3$
• D. $v_{0}t+\frac{1}{3}b{t}^2$

Answer 1

The correct option is A $v_{0}t+\frac{1}{6}b{t}^3$

$a=bt$
$v=\int a\cdot dt=\int bt\cdot dt$
$v\left(t\right)=\frac{b{t}^2}{2}+v_0$
$s=\int v\cdot dt=\frac{b{t}^3}{6}+v_{0}t+0$
$s\left(t\right)\to \frac{b{t}^3}{6}+v_{0}t$