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 #?
The impulse at
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,