A 5 kg cart moving at 2 m/s elastically collides with a stationary 3 kg cart in 1D. What is the final velocity of the 5 kg cart?

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Multiple Choice

A 5 kg cart moving at 2 m/s elastically collides with a stationary 3 kg cart in 1D. What is the final velocity of the 5 kg cart?

Explanation:
In a one-dimensional elastic collision, both momentum and kinetic energy are conserved. When the second cart is initially at rest, the final velocity of the moving cart follows a simple relation: v1' = [(m1 − m2) / (m1 + m2)] × v1. Here, m1 = 5 kg, m2 = 3 kg, and the initial velocity v1 = 2 m/s. So v1' = [(5 − 3) / (5 + 3)] × 2 = (2/8) × 2 = 0.5 m/s. This means the 5 kg cart continues moving forward but more slowly after the collision. For completeness, the second cart ends up at v2' = [2 m1 / (m1 + m2)] × v1 = (10/8) × 2 = 2.5 m/s, preserving momentum and kinetic energy overall.

In a one-dimensional elastic collision, both momentum and kinetic energy are conserved. When the second cart is initially at rest, the final velocity of the moving cart follows a simple relation: v1' = [(m1 − m2) / (m1 + m2)] × v1.

Here, m1 = 5 kg, m2 = 3 kg, and the initial velocity v1 = 2 m/s. So v1' = [(5 − 3) / (5 + 3)] × 2 = (2/8) × 2 = 0.5 m/s. This means the 5 kg cart continues moving forward but more slowly after the collision.

For completeness, the second cart ends up at v2' = [2 m1 / (m1 + m2)] × v1 = (10/8) × 2 = 2.5 m/s, preserving momentum and kinetic energy overall.

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