Question

suppose you are looking at two graphs of velocity vs time. the first graph is of an object undergoing constant positive acceleration of 2 m/s², and the second graph is of an object undergoing constant positive acceleration of 4 m/s². how do the graphs compare? (1 point) both graphs are constant, horizontal lines, but the first graph has a higher constant line than the second graph. both graphs are constant, horizontal lines, but the second graph has a higher constant line than the first graph. both graphs are linear with positive slopes, but the second graph has a steeper slope than the first graph. both graphs are linear with positive slopes, but the first graph has a steeper slope than the second graph.

Explanation:

Step1: Recall acceleration - velocity - time relation

Acceleration is the rate of change of velocity with respect to time. On a velocity - time graph, acceleration is the slope of the graph.

Step2: Analyze the given accelerations

The first object has an acceleration of $2\ m/s^{2}$ and the second has an acceleration of $4\ m/s^{2}$. Since acceleration is positive and constant for both, the velocity is increasing with time for both objects. A non - zero constant acceleration results in a linear velocity - time graph with a positive slope.

Step3: Compare the slopes

The magnitude of the acceleration is equal to the magnitude of the slope of the velocity - time graph. Since $4>2$, the second graph (with an acceleration of $4\ m/s^{2}$) has a steeper slope than the first graph (with an acceleration of $2\ m/s^{2}$).

Answer:

C. Both graphs are linear with positive slopes, but the second graph has a steeper slope than the first graph.