In a one-dimensional perfectly elastic collision, a 5 kg cart moving at 2 m/s collides with a stationary 3 kg cart. What is the final velocity of the 3 kg cart?

• A. 2.0 m/s
• B. 3.0 m/s
• C. 2.25 m/s
• D. 2.5 m/s

Answer: (D)

In a one-dimensional perfectly elastic collision, both momentum and kinetic energy are conserved. When the second object starts from rest, the final velocity of that object is given by v2' = [2 m1 /(m1 + m2)] × v1.

Here, m1 = 5 kg, m2 = 3 kg, and v1 = 2 m/s. So v2' = [2 × 5 /(5 + 3)] × 2 = (10/8) × 2 = 1.25 × 2 = 2.5 m/s.

Thus the 3 kg cart ends up moving at 2.5 m/s. This result aligns with momentum and energy conservation for the system; the other values would not satisfy both conditions simultaneously.