A car with 2 × 10^3 kg moving at a speed of 10 m/s collides and sticks with car B of mass of 3 × 10^3 kg initially at rest. How much kinetic energy is lost during collision?

.

Explanation:

KE lost = Total KE before Collision - Total KE after Collision.

For each car, the KE before collision can simply be found with the equation:

, where

The car would have an initial KE of:

.

The car was initially not moving. Hence, its speed and kinetic energy would zero before the collision.

To find the velocity of the two cars after the collision, apply the conservation of momentum.

The momentum of an object is equal to its mass times its velocity . In other words, .

Let the mass of the two cars be denoted as and , and their initial speeds and . Since the two cars are stuck to each other after the collision, their final speeds would be the same. Let that speed be denotes as .

Initial momentum of the two-car system:

.

After the collision, both car would have a velocity of (since they were stuck to each other.) As a result, the final momentum of the two-car system would be:

.

Since momentum is conserved during the collision, the momentum of the system after the collision would also be . That is: .

Solve for :

.

Hence, the total kinetic energy after the collision would be:

.

The amount of kinetic energy lost during the collision would be:

.

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get