Question

A car travels along the x-axis with increasing speed. We don’t know if to the left or the right. Which of the graphs in Fig. 2–34 most closely represents the motion of the car?

Short answer

The correct option is (a).

Step-by-step solution

Step 1. Significance of the x-t curve of the car

The x-t curve represents the variation between the distance moved and the time taken by the car and can be used to determine the speed or velocity of the car.

In this curve, the y-axis represents the distance traveled, and the x-axis represents the time taken by the car.

Step 2. Analysis of the curve in option (a)

In curve (a), the slope is increasing. The curve gets steeper with time as the slope is initially negative, and then it increases. The car travels in the x-axis direction with an increasing speed. It shows that initially, the speed of the car is slow, and it increases towards the end of motion. This way, the speed of the car increases with time.

Thus, option (a) is correct.

Step 3. Analysis of the curve in option (b)

In curve (b), the slope is larger at the end. The car is moving with constant speed as the graph is a straight line.

Hence, option (b) is incorrect.

Step 4. Analysis of the curve in option (c)

In curve (c), the slope is initially large, and it becomes negative by the end of the motion of the car. So, the speed decreases with time. This curve does not show the motion of the given car.

So, option (c) is incorrect.

Step 5. Analysis of the curve in option (d)

In curve (d), the graph shows that the car speed initially increases but decreases by the motion’s end. This curve does not represent the motion of the car.

So, option (d) is incorrect.

Step 6. Analysis of the curve of option (e)

In curve (e), the graph has a positive slope, indicating the positive speed of the car.

Note that when a car has a constant speed, it is denoted by a constant slope, and when the car has a lesser speed, it is denoted by a lesser slope of the curve. In the given curve, the speed of the car is constant, with a positive slope.

So, option (e) is incorrect.

Step 7. Determination of the correct option.

From the above analysis, curve (a) represents the car moving with increasing speed toward the x-axis. And this most closely shows the motion of the car.

Thus, option (a) is correct.