What is the final velocity of the first vehicle if it collides elastically with a stationary vehicle?

In a perfectly elastic collision, both momentum and kinetic energy are conserved. To find the final velocity of the first vehicle after it collides with a stationary vehicle, we need to apply the principles of conservation of momentum and conservation of kinetic energy.

When one object is moving and collides elastically with another object that is stationary, the final velocity of the moving object can be determined using the equations derived from these conservation laws.

Let's denote:

• (m_1) as the mass of the first vehicle,

• (u_1) as the initial velocity of the first vehicle (before the collision),

• (v_1) as the final velocity of the first vehicle (after the collision),

• (m_2) as the mass of the second vehicle (the stationary one),

• (u_2) as the initial velocity of the second vehicle (which is zero),

• (v_2) as the final velocity of the second vehicle.

In an elastic collision involving two masses, the final velocities can be calculated with the following equations:

1. Momentum Conservation:

[ m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 \