Answer to Question #116231 in Mechanics | Relativity for Rethabile Force

Question

A car with a mass of 1565 kg initially at rest accelerates at a constant rate with a time interval of 9.2s reaches 12 m/s. It then collides with a stationary car with an elastic spring bumper.
What's the final kinetic energy of the system?

Answer 1

Explanations & Calculations

• As the collision starts, total energy the system (moving car & the stationary car) has is the kinetic energy which is gained by the moving car.
• Since the collision is elastic due to the spring being elastic, no kinetic energy is absorbed.
• And as no any information is given regarding the external frictional forces from the surroundings there is no any means of losing energy of the system.
• Therefore, final kinetic energy of the system equals to that which was just before the collision gained by the car in motion.
• What happens after the collision is that, the two cars move in different velocities in a way the system's momentum is kept constant.

Therefore, the kinetic energy (also the final) of the system is,

$\qquad\qquad \begin{aligned} \small E_k &= \small \frac{1}{2}mv^2\\ &= \small \frac{1}{2}\times1565kg\times (12ms^{-1})^2\\ &= \small \bold{112680\,J}\\ &= \small \bold{112.68\,kJ} \end{aligned}$