Question

the velocity-time graphs represent the motion of three different objects. identify any object that is getting faster or speeding up. tap on all that apply. tap to select or deselect graphs.

Explanation:

To determine which objects are speeding up, we analyze the velocity - time graphs:

Step 1: Recall the concept of speeding up

An object is speeding up when the magnitude of its velocity is increasing. This occurs when the velocity and acceleration have the same sign (both positive or both negative). In a velocity - time graph, the slope of the graph represents acceleration. If the velocity is positive (above the time axis) and the slope (acceleration) is positive, or if the velocity is negative (below the time axis) and the slope (acceleration) is negative, the object is speeding up.

Step 2: Analyze the first graph

The first graph has a positive velocity (above the time axis) and a positive slope (since the line is increasing with time). So, the velocity is positive and the acceleration (slope) is positive. This means the magnitude of the velocity is increasing, and the object is speeding up.

Step 3: Analyze the second graph

The second graph has a negative velocity (below the time axis) and a negative slope (the line is decreasing further with time, so the slope is negative). Since the velocity and acceleration (slope) have the same sign (both negative), the magnitude of the velocity is increasing (it is becoming more negative, so the speed, which is the magnitude of velocity, is increasing). Thus, this object is also speeding up.

Step 4: Analyze the third graph

The third graph has a negative velocity (below the time axis) and a positive slope (the line is moving towards the time axis, so the slope is positive). Here, the velocity is negative and the acceleration (slope) is positive. The signs of velocity and acceleration are different, so the magnitude of the velocity is decreasing (it is moving towards zero), and the object is slowing down.

Answer:

The first and the second velocity - time graphs (the objects represented by these graphs) are speeding up.