An objects speed is increased by a factor of three. What does this do to its kinetic energy? The kinetic energy increases, but less than by a factor of two. The kinetic energy increases by a factor of three. The kinetic energy cannot be determined. The kinetic energy increases by a factor of two. It does not affect the kinetic energy. The kinetic energy increases by more than a factor of three.
The Correct Answer and Explanation is:
The correct answer is: The kinetic energy increases by more than a factor of three.
Explanation:
Kinetic energy (KE) is given by the equation:KE=12mv2KE = \frac{1}{2} m v^2KE=21mv2
Where:
- mmm is the mass of the object.
- vvv is the velocity (speed) of the object.
If the speed of the object is increased by a factor of three, we are changing vvv in the kinetic energy formula.
Let’s say the initial speed is v1v_1v1 and the initial kinetic energy is:KE1=12mv12KE_1 = \frac{1}{2} m v_1^2KE1=21mv12
Now, if the speed is increased by a factor of three, the new speed is v2=3v1v_2 = 3v_1v2=3v1. The new kinetic energy is:KE2=12m(3v1)2=12m⋅9v12=9(12mv12)=9KE1KE_2 = \frac{1}{2} m (3v_1)^2 = \frac{1}{2} m \cdot 9v_1^2 = 9 \left( \frac{1}{2} m v_1^2 \right) = 9 KE_1KE2=21m(3v1)2=21m⋅9v12=9(21mv12)=9KE1
So, the kinetic energy increases by a factor of nine when the speed increases by a factor of three. This shows that kinetic energy is proportional to the square of the velocity, meaning that if the speed increases by a factor of nnn, the kinetic energy increases by a factor of n2n^2n2. Therefore, when the speed is tripled, the kinetic energy increases by a factor of nine, not three.
This relationship highlights the non-linear dependence of kinetic energy on speed. As the speed increases, the kinetic energy increases much more rapidly due to the squared term in the kinetic energy formula.
