Question

We set the origin of a coordinate system so that the position of a train is x=0 mx=0 m at t=0 st=0 s. Figure P2.22 shows the train’s velocity graph.

A. Draw position and acceleration graphs for the train.
B. Find the acceleration of the train at t=3.0 st=3.0 s.

Answer 1

A. The position graph for the train is a parabola, and the acceleration graph is a horizontal line.

B. The acceleration of the train at t=3.0 s is zero.

Step-by-step explanation:

A. The position graph can be obtained by integrating the velocity graph. Since the velocity graph is a straight line, the position graph will be a parabola. The acceleration graph is the derivative of the velocity graph. In this case, as the velocity is constant, the acceleration is zero. The position-time graph will resemble a parabola because the velocity is constant, leading to uniform acceleration. The acceleration-time graph will be a horizontal line at zero, indicating constant acceleration.

B. To find the acceleration at t=3.0 s, we look at the acceleration graph. As mentioned earlier, the acceleration is a constant value of zero. Therefore, at t=3.0 s, the acceleration of the train is zero. This means that at this particular instant, the train is not accelerating or decelerating; its velocity remains constant.

In summary, the position-time graph will be a parabola, and the acceleration-time graph will be a horizontal line at zero. At t=3.0 s, the acceleration of the train is zero, indicating that the train maintains a constant velocity at that specific moment.