Question

a point particle starting from rest has a velocity that increases linearly with time such that v = pt where p=4m/s^2. The distance covered in 2 second is​

Answer 1

Given :

Velocity equation of particle is given by v = pt where p = 2m/s²

Initial velocity = zero

To Find :

Distance covered by particle in 2s.

Solution :

In order to find distance covered by particle, we have to integrate the given velocity equation.

Mathematically,

$\dag\:\:\boxed{\tt{\orange{\displaystyle d=\int\:v\:dt}}}$

By substituting the given values,

$\displaystyle:\implies\sf\:d=\int\:v\:dt$

$\displaystyle:\implies\sf\:d=\int\:(pt)\:dt$

ATQ, value of p is 2

$\displaystyle:\implies\sf\:d=\int\:2t\:dt$

$\displaystyle:\implies\sf\:d=\bigg[\dfrac{2t^2}{2}\bigg]$

$:\implies\sf\:d=\big[{t^2}\big]_{0}^{2}$

$:\implies\sf\:d=(2)^2-(0)^2$

$:\implies\:\underline{\boxed{\bf{\purple{d=4\:m}}}}$