A cat walks in a straight line, which we shall call the x-axis, with the positive direction to the right. You take measurements of the cat’s velocity as a function of time and graph it below

Question

i. What is the cat's acceleration at t = 2s and t = 5s

ii. How far did the cat move in the first 6s and in which direction

iii. Sketch the acceleration vs. time graph of the cat's motion

Answer 1

Acceleration is the slope of the velocity curve. Since the slope is the same between 0 and 6 seconds, the acceleration is the same. To determine it, make a slope triangle and use the slope equation. For the points (0, 8) and (6, 0) the slope = (y₂ - y₁)/(x₂ - x₁) = (0 - 8)/(6 - 0) = -4/3 cm/s²

Distance is the area under the velocity curve. Between 0 and 6 seconds, a triangle is formed by the "curve" so the area = (1/2)bh = (1/2)(6)(8) = 24 cm. The answer is positive so the direction is positive, or, to the right.

Based on my comment above about acceleration, the graph is a straight horizontal line where acceleration = -4/3 cm/s² between t = 0 and t = 6 seconds