Finding Impulse and Momentum on a Frictionless Surface

[Tubs]

I can't seem to get past this one, and it should be possible to solve without using integration. Any help would be great :D

A 0.25 kg object is stationary on a frictionless surface. At t = 0, a horizontal force begins to move the object. The force is given by F = (12 - 3t^2) and acts until its magnitude is zero.

a) What is the magnitude of the impulse between t = 0.5 and t = 1.25 s?
b) What is the change in momentum from when the object is stationary to when the magnitude of the force is zero?

 

[mezarashi]

I really don't see how this one can be solved without calculus. The force is not constant, meaning the acceleration is not constant. None of the elementary kinematics equations will apply. Only the differential form of Newton's 2nd law should be used.

 

[dx]

Force is not constant. You have to integrate.

 

[Tubs]

Ok, thanks a lot. Another quick one that I am stumped on:

A thin rod rotates around one end. Its angular acceleration is 3/2 radians / second^2 and has a rotational kinetic energy of 1.60 J at t = 4s. What is the kinetic energy at t = 0s?

A graph was given of this question, pretty much modeling a straight line on velocity / time graph. At t = 0 the velocity looks to be about 1.4 if that helps :)

 

[andrevdh]

Use the fact that that the ratio of the rotational kinetic energies at two different times are equal to the ratio of the square of the angular velocities at these times. Then by $v=\omega r$ the r's cancel. So you are left only with the velocities squared, which can be determined with the graph.