Question

The acceleration of a particle can be expressed as a(t)= 12-4t^2. If the particle velocity is v(0)=50, the. What is the velocity at t=6

Answer 1

The velocity at t = 6 is of -166 units of velocity.

Explanation:

Velocity function:

The velocity function is the integral of the acceleration function.

We have that:

The acceleration function is:

`a(t) = 12 - 4t^2`

So the velocity function is:

`v(t) = \int a(t) dt = \int (12 - 4t^2) dt = 12t - (4t^3)/(3) + K`

In which K is the constant of integration, which is v(0).

v(0)=50

This means that:

`v(t) = 12t - (4t^3)/(3) + 50`

What is the velocity at t=6?

`v(6) = 12*6 - (4*6^3)/(3) + 50 = -166`

The velocity at t = 6 is of -166 units of velocity.