A moving car has kinetic energy.

If it speeds up until it is going four times
faster than before, how much kinetic energy
does it have in comparison?
1. The mass is needed.
2. The same
3. Sixteen times larger
4. Four times smaller
5. Four times larger
6. Sixteen times smaller

sixteen times larger

To determine the kinetic energy of the car at different speeds, we need to utilize the formula for kinetic energy: KE = (1/2)mv^2, where m represents the mass of the car and v represents its velocity.

Given that the car is moving four times faster than before, we can say that its new velocity is four times the initial velocity (v_new = 4v_initial).

Now, let's consider the options:

1. The mass is needed: This is true since the kinetic energy formula requires the mass of the object.

2. The same: This cannot be correct since the car's velocity has increased.

3. Sixteen times larger: To determine if the kinetic energy is sixteen times larger, we need to calculate the ratio of the new kinetic energy to the initial kinetic energy.
KE_new = (1/2)m(4v_initial)^2
= (1/2)m(16v_initial^2)
= 8mv_initial^2

This shows that the kinetic energy at the new speed is eight times larger than the initial kinetic energy, but not sixteen times larger.

4. Four times smaller: This is incorrect since the kinetic energy increases with the square of the velocity. Increasing the velocity by a factor of four results in a sixteen-fold increase, not a decrease.

5. Four times larger: This is the correct answer since increasing the velocity by a factor of four results in a sixteen-fold increase in kinetic energy (KE_new = 16KE_initial).

6. Sixteen times smaller: This is not correct since increasing velocity leads to an increase in kinetic energy, not a decrease.

Therefore, the correct answer is option 5. The kinetic energy of the car is four times larger when it is moving four times faster than before.