Fig. 21.1 shows two trolleys, A and B, on a frictionless track. Trolley A is given a push and moves toward stationary trolley B. A motion sensor records the...

(a) Initial speed of trolley B [1]

Trolley B is stationary before the collision, so its initial speed is 0 m/s. [1]

(b) Type of collision [1]

When A stops completely and B moves off at A's original speed, both momentum and kinetic energy are conserved. This is an elastic collision. [1]

In an elastic collision between two objects of equal mass where one is initially stationary, the moving object stops and the stationary one moves off with the same speed. This is a classic result of simultaneous conservation of momentum and kinetic energy.

(c) Distance-time graph for trolley A [2]

Before the collision: Trolley A moves at constant speed, so its distance-time graph is a straight line with a positive (constant) gradient. [1]

After the collision: Trolley A is stationary, so its distance remains constant. The graph is a horizontal line. [1]

(d) Kinetic energy of A before the collision [2]

\( KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 0.50 \times 2.0^2 \) [1]

\( KE = \frac{1}{2} \times 0.50 \times 4.0 = 1.0 \text{ J} \) [1]

(e) Kinetic energy of B after the collision [1]

Since this is an elastic collision, kinetic energy is conserved. Trolley B moves at 2.0 m/s with the same mass as A, so its kinetic energy is 1.0 J. [1]

You can verify: \( KE_B = \frac{1}{2} \times 0.50 \times 2.0^2 = 1.0 \text{ J} \), confirming no kinetic energy was lost.