Question

The position of an object moving along $x-$axis is given by $x=a+b{t}^2$ where $a=8.5m$, $b=2.5m{s}^{-2}$ and $t$ is measured in seconds. What is its velocity at $t=0s$ and $t=2.0s$. What is the average velocity between $t=2.0s$ and $t=4.0s$.

Answer 1

Velocity is $\frac{dx}{dt}=0+2bt=2bt=5t$, after putting $b=2.5$

Velocity at $t=0$ is $v=5\times 0=0$

Velocity at $t=2sec$ is $v=5\times 2=10m/s$

$x$ at $t=2sec$ is $x=8.5+2.5(2{)}^2=18.5meter$

$x$ at $t=4sec$ is $x=8.5+2.5(4{)}^2=48.5meter$

so the displacement between $t=2$ and $t=4$ is $48.5-18.5=30meter$

so average velocity will be $\frac{displacement}{time}=\frac{30m}{(4-2)sec}=15m/s$