Question

1. -/3 points parts (a), (b), and (c) of the figure below represent three graphs of the velocities of different objects moving in straight - line paths as functions of time. the possible accelerations of each object as functions of time are shown in parts (d), (e), and (f). match each velocity vs. time graph with the acceleration vs. time graph that best describes the motion.

Explanation:

Step1: Recall acceleration - velocity relationship

Acceleration is the derivative of velocity with respect to time. A straight - line velocity - time graph with a constant slope has a constant acceleration. A curved velocity - time graph has a non - constant acceleration.

Step2: Analyze graph (a)

Graph (a) is a straight - line velocity - time graph with a constant positive slope. So, the acceleration is constant and positive. It matches with acceleration graph (d) which is a horizontal line above the time - axis.

Step3: Analyze graph (b)

Graph (b) is a curved velocity - time graph with an increasing slope. So, the acceleration is increasing. It matches with acceleration graph (e) which is a horizontal line (constant non - zero acceleration) for some time and then increases.

Step4: Analyze graph (c)

Graph (c) has a straight - line part with a positive slope (constant positive acceleration) followed by a horizontal part (zero acceleration). It matches with acceleration graph (f) which has a non - zero constant value for some time and then drops to zero.

Answer:

(a) - (d), (b) - (e), (c) - (f)