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Question

A box proceeds along the x-axis and the figure below shows a record of its velocity as a function of time. Every gridline along the vertical axis corresponds to 2.00 m/s and each gridline along the horizontal axis corresponds to 0.500 s. (Enter your answers in m/s². Indicate the direction with the signs of your answers. Note that t = 0

 at the intersection of the axes.)

(a) Determine the average acceleration of the box in the time interval t = 0

 to t = 2.50 s.

b) Determine the average acceleration of the box in the time interval t = 2.50 s

 to t = 7.50 s.

c) Determine the average acceleration of the box in the time interval t = 0

 to t = 10.0 s.

Answer 1

The average acceleration over an interval of time is defined as the net change in velocity (v₂ - v₁) divided by the time interval. Use the graph to determine the velocity at the beginning (v₁) and the end (v₂) of the time intervals described in each part of the question, determine the change in velocity as v₂ - v₁, and divide that change in velocity by the associated time interval. The time intervals will be 2.5 s, 5.0 s, and 10.0 s respectively.

Note that the mathematical operation you perform to find average acceleration is identical to the calculation of the slope of the line segment drawn from point 1 to point 2 on the graph.

Note also that the average acceleration over a given interval of time will be positive when v₂ is greater than v₁, and negative when v₂ is less.