# Kinetic Energy speed and a car

• fizz123
In summary, the original speeds of the two cars were v1 = v2 and v1 + 8.5 = v2 + 8.5. This was determined by setting up the conditions properly, where one car has twice the mass of the other and only half as much kinetic energy. By increasing their speeds by 8.5 m/s, both cars then have the same kinetic energy.
fizz123
One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 8.5 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?

first i set it up like this:
.5 * m * v1^2 = .5 * (.5 * 2m * v2^2)

then i get:
v1 = v2

then
.5 * m * (v1 + 8.5)^2 = .5 * 2m * (v2 + 8.5)^2
.5 * (v1 + 8.5)^2 = (v2 + 8.5)^2

but its not right...

1) "One car has twice the mass of a second car" $$m_{1}=2m_{2}$$
2) "but only half as much kinetic energy" $$K_{1}=\frac{K_{2}}{2}$$
3)"When both cars increase their speed by 8.5 m/s, they then have the same kinetic energy":
$$\frac{m_{1}}{2}(v_{1}+8.5)^{2}=\frac{m_{2}}{2}(v_{2}+8.5)^{2}, K_{1}=\frac{m_{1}}{2}v_{1}^{2},K_{2}=\frac{m_{2}}{2}v_{2}^{2}$$

$$K_{1}=\frac{2m_{2}}{2}v_{1}^{2}=\frac{m_{2}}{4}v_{2}^{2}=\frac{K_{2}}{2}$$

Thus, we have: $${v}_{1}=\frac{v_{2}}{2}$$

Last edited:
thank you, i got it now

Howcome both masses are over 2?

## 1. What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is directly proportional to the object's mass and the square of its velocity.

## 2. How is kinetic energy related to speed?

Kinetic energy is directly proportional to the square of an object's velocity. This means that as an object's speed increases, its kinetic energy also increases.

## 3. How does a car's speed affect its kinetic energy?

A car's kinetic energy is affected by its speed due to the direct relationship between speed and kinetic energy. As a car's speed increases, its kinetic energy also increases.

## 4. What is the formula for calculating kinetic energy?

The formula for calculating kinetic energy is KE = 1/2 * m * v^2, where KE is kinetic energy, m is the mass of the object, and v is the velocity or speed of the object.

## 5. How does kinetic energy impact a car's braking distance?

Kinetic energy plays a significant role in a car's braking distance. The higher the car's kinetic energy, the longer the braking distance will be. This is because more energy needs to be dissipated in order to slow down the car's motion.

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