A mass m is accelerated by a time-varying force e-Btv³, where v is its velocity. It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore dv m- = dt -βίν- ην.

A student throws an object of mass m straight up in the air with initial velocity vo, and the object reaches its maximum height in a time t. Ignoring the effects of air resistance, which of the following statements must be true? (There may be more than one correct answer.) When the object is in the student's hand, the reaction force to the normal force is the weight of the object. The object travels a distance vot over this time interval The object's acceleration is vo/t The average speed of the object over this time interval is vo/2 When the object is in the air, the object exerts a force on the earth with a magnitude mg.

You have been hired as an expert witness in a court case involving an automobile accident. A piece of a bullet was found in the accident. The force on the bullet is given by the formula F=580 – (1.80 x 10^5)t over the time interval t=0 to t = 3.0 x 10^-3s. In this formula, t is in seconds and F is in newtons. (i) Sketch a graph of F vs. t for t=0 to t = 3.0 ms.   (ii) Using graphical methods, estimate the impulse given by the bullet. (iii) As a result of this impulse, the bullet achieves a speed of 220 ms-1, given to it in the barrel of a gun, what must its mass be? (iv) The accident involved car A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Determine the velocity for each car after the collisions.