A train traveling at 4.0 m/s changes its speed to 2.0 m/s.Which graph shows the change in the kinetic energy of the train?

To determine which graph accurately shows the change in the kinetic energy of the train as it slows down from 4.0 m/s to 2.0 m/s, we first need to calculate the kinetic energy at both speeds using the formula for kinetic energy:

1. Break Down the Problem

We will calculate the kinetic energy before and after the speed change.

2. Relevant Concepts

The formula for kinetic energy (KE) is given by: $KE = \frac{1}{2}mv^2$ where $m$ is the mass of the object and $v$ is its speed.

3. Analysis and Detail

Since we do not have the mass of the train, we can keep it as $m$ for our calculations:

• Initial Kinetic Energy at 4.0 m/s: $KE_{initial} = \frac{1}{2}m(4.0)^2 = \frac{1}{2}m(16) = 8m$

• Final Kinetic Energy at 2.0 m/s: $KE_{final} = \frac{1}{2}m(2.0)^2 = \frac{1}{2}m(4) = 2m$

• Change in Kinetic Energy: $\Delta KE = KE_{final} - KE_{initial} = 2m - 8m = -6m$

4. Verify and Summarize

The change in kinetic energy is negative, indicating a decrease in kinetic energy as the train slows down.

Final Answer

The change in kinetic energy of the train is $-6m$, indicating a decrease. The graph that shows a decrease in kinetic energy from a higher value to a lower value should accurately represent this scenario.