Question

If the initial speed of particle is u and it's acceleration is given as a=At^3, where A is constant and t is time, then it's final speed v will be?

Answer 1

Answer

Given acceleration a=At^3

As we know that acceleration

a=dv/dt

At^3=dv/dt

At^3dt=dv

Integral on both sides now then

V=At^4/4

Hope u get it

Answer 2

Answer:

The final speed v will be $\dfrac{At^4}{4}+C$

Explanation:

Given that,

Initial speed = u

Acceleration $a = At^3$

Velocity :

The velocity is the rate of change of the position of the particle.

$v = \dfrac{dx}{dt}$

Acceleration :

Acceleration is the rate of change of the velocity of the particle.

$a=\dfrac{dv}{dt}$

We need to calculate the speed of the particle

The acceleration of the particle is

$a =\dfrac{dv}{dt}$

$dv=a dt$

$dv=At^3 dt$

On integrating of both sides

$\int{dv}=\int{At^3}dt$

$v=\dfrac{At^4}{4}+C$

Hence, The final speed v will be $\dfrac{At^4}{4}+C$