Question

Why doesn't the car with greater velocity have more kinetic energy than another car which moves slowly but has a smaller mass and bigger acceleration?

Answer 1

The kinetic energy of an object depends on both its mass and its velocity. The formula for kinetic energy is:

$KE=\frac{1}{2}\cdot m\cdot v^2$

In your scenario, you mentioned a car with greater velocity and another car with a smaller mass and a larger acceleration.

Let's consider two cars:

Car A: Greater velocity, smaller mass Car B: Slower velocity, larger acceleration

Even though Car A has a greater velocity, it does not necessarily mean that it will have more kinetic energy than Car B. The kinetic energy also depends on the mass of the object.

In the kinetic energy formula, the mass ($m$) is squared, while the velocity ($v$) is only squared once. This means that the mass has a more significant impact on the kinetic energy than the velocity.

If Car A has a greater velocity but a smaller mass, the smaller mass will reduce the overall kinetic energy compared to Car B, which has a larger mass.

Additionally, you mentioned that Car B has a larger acceleration. The acceleration affects the rate at which the velocity changes, but it doesn't directly impact the kinetic energy. The kinetic energy depends on the final velocity, regardless of how the object reaches that velocity.

In summary, the kinetic energy depends on both the mass and the velocity of an object. Having a greater velocity alone does not guarantee that an object will have more kinetic energy. The mass plays a significant role, and even a smaller mass with a greater acceleration may have less kinetic energy compared to an object with a larger mass and a slower velocity.