Two model cars \(A\) and \(B\) have masses 200 grams and \(k\) grams respectively. They move towards each other in a straight line and collide directly when their speeds are \(5 \mathrm {~ms} ^ { - 1 }\) and \(4 \mathrm {~ms} ^ { - 1 }\) respectively. As a result the speed of \(A\) is reduced to \(2 \mathrm {~ms} ^ { - 1 }\), in the same direction as before. The direction of \(B\) 's motion is reversed and its speed immediately after the impact is \(5 \mathrm {~ms} ^ { - 1 }\).
Find the magnitude of the impulse exerted by \(A\) on \(B\) in the impact. State the units of your answer.
Find the value of \(k\).
The surface on which the cars move is rough, and \(B\) comes to rest 3 seconds after the impact. The coefficient of friction between both cars and the surface is \(\mu\).
Find the value of \(\mu\).
Find the distance travelled by \(A\) after the impact before it comes to rest.