Does the KE of a car change more when it goes from 10 to 20 km/h or when it goes from 20 to 30 km/h?

20 to 30 km/h

KE=1/2 × m × v^2
Velocity is squared higher you go bigger difference

The kinetic energy (KE) of an object depends on its mass and speed. The formula for calculating kinetic energy is KE = (1/2) * m * v^2, where m is the mass of the object and v is its velocity.

To determine which speed change results in a greater change in kinetic energy for a car, we can compare the KE at the initial and final speeds.

Assuming the mass of the car remains constant, let's calculate the KE at each speed increment:

When the car goes from 10 to 20 km/h:
- Initial speed (vi) = 10 km/h
- Final speed (vf) = 20 km/h

The change in speed (Δv) = vf - vi = 20 - 10 = 10 km/h

Therefore, the change in kinetic energy (ΔKE) when the car goes from 10 to 20 km/h is:
ΔKE = (1/2) * m * Δv^2

When the car goes from 20 to 30 km/h:
- Initial speed (vi) = 20 km/h
- Final speed (vf) = 30 km/h

The change in speed (Δv) = vf - vi = 30 - 20 = 10 km/h

Therefore, the change in kinetic energy (ΔKE) when the car goes from 20 to 30 km/h is also:
ΔKE = (1/2) * m * Δv^2

Comparing these two equations, we can observe that the change in kinetic energy is proportional to the square of the velocity change (Δv^2).

Since the speed change is the same in both cases (Δv = 10 km/h), the change in kinetic energy will be the same in magnitude. Therefore, the KE of a car changes by the same amount when it goes from 10 to 20 km/h as when it goes from 20 to 30 km/h.

To determine whether the kinetic energy (KE) of a car changes more when it goes from 10 to 20 km/h or when it goes from 20 to 30 km/h, we need to understand the formula for calculating kinetic energy.

The formula for kinetic energy is:
KE = 1/2 * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

Now, let's compare the changes in kinetic energy for both scenarios:

1. From 10 to 20 km/h:
First, we need to assume that the mass of the car remains constant. So, only the velocity changes.

Initial velocity (v1) = 10 km/h
Final velocity (v2) = 20 km/h

To find the change in kinetic energy, we need to calculate KE2 - KE1:

KE2 = 1/2 * m * v2^2 = 1/2 * m * (20^2)
KE1 = 1/2 * m * v1^2 = 1/2 * m * (10^2)

Change in KE = KE2 - KE1

2. From 20 to 30 km/h:
Using the same logic as above:

Initial velocity (v1) = 20 km/h
Final velocity (v2) = 30 km/h

KE2 = 1/2 * m * v2^2 = 1/2 * m * (30^2)
KE1 = 1/2 * m * v1^2 = 1/2 * m * (20^2)

Change in KE = KE2 - KE1

By calculating the actual values of KE2 - KE1 for both scenarios, we can determine which change in kinetic energy is greater.

20 to 30

KE=(1/2)(m)(v^2)
velocity is squared, bigger difference higher you go