Multiple Choice
A car slows down from to in . What is its acceleration?
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2. 1D Motion / Kinematics
Intro to Acceleration
Multiple Choice
If the speed of your car is doubled, how does its (kinetic energy) change?
A
The decreases by half.
B
The remains the same.
C
The increases by a factor of .
D
The doubles.
Verified step by step guidance1
Recall the formula for kinetic energy: \(\text{KE} = \frac{1}{2} m v^{2}\), where \(m\) is the mass of the car and \(v\) is its speed.
Identify the initial kinetic energy as \(\text{KE}_1 = \frac{1}{2} m v^{2}\).
When the speed is doubled, the new speed becomes \$2v$. Substitute this into the kinetic energy formula to get the new kinetic energy: \(\text{KE}_2 = \frac{1}{2} m (2v)^{2}\).
Simplify the expression for \(\text{KE}_2\): \(\text{KE}_2 = \frac{1}{2} m \times 4v^{2} = 4 \times \frac{1}{2} m v^{2} = 4 \times \text{KE}_1\).
Conclude that doubling the speed results in the kinetic energy increasing by a factor of 4.
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