Question

A particle is moving in a straight line so that after $t$ seconds its distance is $s\left(\text{in}cms\right)$ from a fixed point on the line is given by $s=f\left(t\right)=8t+t^3$.Find:
1.the velocity at time $t=2\sec$
2.the initial velocity
3.acceleration at $t=2sec$

Answer 1

Given displacement of the particle is $s=f\left(t\right)=8t+t^{3}cm$

Velocity of particle at time $t$ is $v=f^{\prime }\left(t\right)=8+3t^{2}cm/sec$

$1)$Velocity of particle at time $t=2$ sec is $v=8+3(2{)}^3=32cm/sec$

$2)$Initial velocity is $v=8+3(0{)}^3=8cm/sec$

Acceleration of particle at time $t$ is $\frac{dv}{dt}=6tcm/s^2$

$3)$Acceleration at $t=2$ sec is $a=6\left(2\right)=12cm/s^2$