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 A has the higher kinetic energy because of its mass.
B.
Car B has the higher kinetic energy because of its mass.
C.
Car B has the higher kinetic energy because of its speed.
D.
Car A has the higher kinetic energy because of its speed.

Answer 1

The kinetic energy (KE) of an object can be calculated using the formula:

\[ KE = \frac{1}{2} mv^2 \]

where \(m\) is the mass and \(v\) is the speed of the object.

For Car A:

• Mass \(m_A = 0.245 , \text{kg}\)
• Speed \(v_A = 10 , \text{cm/s} = 0.1 , \text{m/s}\) (since 1 cm = 0.01 m)

Calculating the kinetic energy for Car A: \[ KE_A = \frac{1}{2} (0.245) (0.1)^2 = \frac{1}{2} (0.245) (0.01) = 0.001225 , \text{J} \]

For Car B:

• Mass \(m_B = 0.245 , \text{kg}\)
• Speed \(v_B = 20 , \text{cm/s} = 0.2 , \text{m/s}\)

Calculating the kinetic energy for Car B: \[ KE_B = \frac{1}{2} (0.245) (0.2)^2 = \frac{1}{2} (0.245) (0.04) = 0.0049 , \text{J} \]

Now, let's compare the kinetic energies:

• \(KE_A = 0.001225 , \text{J}\)
• \(KE_B = 0.0049 , \text{J}\)

Car B has a higher kinetic energy because it has the same mass as Car A but travels at a faster speed. Therefore, the correct answer is:

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