Two solar powered toy cars are shown below.

Question

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.