# The velocity of an object with a mass of #2 kg# is given by #v(t)= 3 t^2+ 2 t +8#. What is the impulse applied to the object at #t= 4 #?

##### 1 Answer

Jan 15, 2016

#### Answer:

The impulse at

#### Explanation:

Impulse is equal to the rate of change of momentum:

In this instance the mass is constant so

The instantanteous rate of change of the velocity is simply the slope (gradient) of the velocity-time graph, and can be calculated by differentiating the expression for the velocity:

Evaluated at t = 4, this gives

To find the impulse, then,