Question

The displacement of a particle moving along x - axis is given by x = 18t + 5t${}^2$ calculate the instantaneous velocity at t = 25. Average velocity at t = 25 and t = 35.

Answer 1

Instantaneous velocity is given as time derivative of $dispalcement$ which is $v=dx/dt=18+10t$

Put $t=25$ we get $v=268unit$

Average velocity, $=\frac{\text{Net displacement}}{\text{time taken}}=$

Position at time $t=0$ is $x=0$

Position at time $t=25$ is $x=3575unit$

So displacement in time interval of $25seconds$ is $3575-0=3575unit$

So Average velocity$=3575/25=143unit$

Position at $t=35s$ is $x=6755unit$

So Average velocity at $t=35s$ is $6755/35=193unit$