Speed

Day 1: Forces and Motion of the Bus

Problem 1

In Speed, the bus must remain above a certain speed to avoid triggering the bomb. Suppose the bus increases its speed from \(v_i = 18\ {\rm m/s}\) to \(v_f = 23\ {\rm m/s}\) in \(\Delta t = 7.0\ {\rm s}\).

(a) What is the average acceleration of the bus?

(b) How far does the bus travel during this time? Assume the acceleration is constant.

Problem 2

The bus must round corners at high speed without skidding. Suppose the bus travels at \(v = 22\ {\rm m/s}\) while turning along a curve of radius \(r = 85\ {\rm m}\).

(a) What centripetal acceleration is required?

(b) If the bus mass is \(m = 1.3\times 10^4\ {\rm kg}\), what centripetal force is required?

(c) If the road is flat, what minimum coefficient of static friction is needed to keep the bus from sliding?

Problem 3

At one point the driver must brake hard to avoid danger. Suppose the bus is traveling at \(v_i = 25\ {\rm m/s}\) and brakes uniformly to \(v_f = 20\ {\rm m/s}\) over a distance of \(\Delta x = 42\ {\rm m}\).

(a) What is the acceleration of the bus?

(b) How long does the braking take?

Day 2: Impulse, Energy, and the Jump Scene

Problem 4

Passengers standing on the bus can be thrown off balance when the bus accelerates. Suppose a standing passenger of mass \(m = 72\ {\rm kg}\) experiences a forward acceleration of \(a = 1.8\ {\rm m/s^2}\).

(a) What horizontal net force is required to accelerate the passenger with the bus?

(b) If the passenger’s shoes can provide a maximum static friction force of \(120\ {\rm N}\), will the passenger remain standing without slipping? Assume the floor is horizontal.

Problem 5

The bus jump scene can be treated as projectile motion. Suppose the bus leaves the edge of the gap moving horizontally at \(v_x = 21\ {\rm m/s}\). The far side of the road is horizontally \(\Delta x = 16\ {\rm m}\) away and is \(1.5\ {\rm m}\) lower than the takeoff point. Take \(g = 9.81\ {\rm m/s^2}\) and neglect air resistance.

(a) How long does it take the bus to reach the far side horizontally?

(b) How far does the bus fall during that time?

(c) Based on your result, does the bus clear the gap?

Problem 6

Suppose the bus lands after the jump with speed components \(v_x = 21\ {\rm m/s}\) and \(v_y = -5.4\ {\rm m/s}\). The total mass of the bus is \(m = 1.3\times 10^4\ {\rm kg}\). Use only the vertical component of motion for part (c).

(a) What is the magnitude of the landing speed?

(b) What is the kinetic energy of the bus just before landing?

(c) If the suspension compresses by \(d = 0.30\ {\rm m}\) during the landing and all of the vertical kinetic energy is absorbed during this compression, what is the average upward force from the road on the bus due to the vertical motion alone?