Question

How to find the velocity of the car after collision?

Answer 1

The collision can be elastic or inelastic. Elastic collision obeys both conservations of momentum and kinetic energy but inelastic collision doesn’t obey conservation of kinetic energy. The collision of cars falls under Inelastic collision where kinetic energy is not conserved. Inelastic collision obeys Conservation of Momentum. So we can say that momentum before collision=momentum after the collision.

Complete answer:
The term Momentum refers to a quantity that a moving object possesses. It is defined as the product of mass and velocity and its units are $kgm{s^{ - 1}}$ or $Ns$ . It is represented by the letter. In the given question collision of the car is an inelastic collision that obeys conservation of momentum.
Momentum $P = m \times v$, where m is the mass of the object and $v$ is the velocity of the object.
By conservation of momentum,
Momentum before collision = Momentum after collision
Lets us assume ${m_1}$ and ${v_1}$ be the mass and velocity of the car before collision, ${m_2}$ and ${v_2}$ be the mass and velocity of the colliding object before the collision and ${v_f}$ be the final velocity. Then,
$\Rightarrow {m_1} \times {v_1} + {m_2} \times {v_2} = \left( {{m_1} + {m_2}} \right) \times {v_f}$
If the initial mass and velocity of the car and the colliding object are given we can easily find the velocity of the car after collision from the below equation.
$\Rightarrow {v_f} = \dfrac{{{m_1} \times {v_1} + {m_2} \times {v_2}}}{{{m_1} + {m_2}}}$

Note: Understand what is elastic collision and inelastic collision. Try to derive the equations using conservation of mass for the inelastic collision. If the collision is elastic, use both conservation of momentum and conservation of kinetic energy, then equate both equations to get the final velocity.