Question

Two solar powered toy cars are shown below.



Car A has a mass of 0.245 kg and travels at a speed of 10 cm/s. Car B has a mass of 0.245 kg and travels at a speed of 20 cm/s. Which of the following correctly describes the kinetic energy of the cars?
A.
Car B has the higher kinetic energy because of its speed.
B.
Car B has the higher kinetic energy because of its mass.
C.
Car A has the higher kinetic energy because of its mass.
D.
Car A has the higher kinetic energy because of its speed.

Answer 1

To determine which car has the higher kinetic energy, we can use the formula for kinetic energy (KE):

\[
KE = \frac{1}{2} m v^2
\]

where \(m\) is mass and \(v\) is speed.

For Car A:
- Mass (\(m_A\)) = 0.245 kg
- Speed (\(v_A\)) = 10 cm/s = 0.1 m/s (converting to meters for standard units)

\[
KE_A = \frac{1}{2} \times 0.245 \, \text{kg} \times (0.1 \, \text{m/s})^2
\]
\[
KE_A = \frac{1}{2} \times 0.245 \times 0.01
\]
\[
KE_A = \frac{1}{2} \times 0.00245
\]
\[
KE_A = 0.001225 \, \text{J}
\]

For Car B:
- Mass (\(m_B\)) = 0.245 kg
- Speed (\(v_B\)) = 20 cm/s = 0.2 m/s

\[
KE_B = \frac{1}{2} \times 0.245 \, \text{kg} \times (0.2 \, \text{m/s})^2
\]
\[
KE_B = \frac{1}{2} \times 0.245 \times 0.04
\]
\[
KE_B = \frac{1}{2} \times 0.0098
\]
\[
KE_B = 0.0049 \, \text{J}
\]

Now we compare the kinetic energies:
- \(KE_A = 0.001225 \, \text{J}\)
- \(KE_B = 0.0049 \, \text{J}\)

Since \(KE_B > KE_A\), we conclude that:

**A. Car B has the higher kinetic energy because of its speed.**