1.) Find the instantaneous velocity at 0.5 s. Answer in units of m/s 2.) Find th

Question

1.) Find the instantaneous velocity at 0.5 s.
Answer in units of m/s

2.) Find the instantaneous velocity at 6.5 s.
Answer in units of m/s

3.) Find the average velocity between 0 s and 3 s.
Answer in units of m/s

4.) Find the average velocity over the whole time
shown.
Answer in units of m/s

The position versus time for a certain object moving along the x-axis is shown. The object?s initial position is ?4 m. 1.) Find the instantaneous velocity at 0.5 s. Answer in units of m/s 2.) Find the instantaneous velocity at 6.5 s. Answer in units of m/s 3.) Find the average velocity between 0 s and 3 s. Answer in units of m/s 4.) Find the average velocity over the whole time shown. Answer in units of m/s

Explanation / Answer

First of all, we know that instantaneous velocity is the derivative of position, so we are looking for slopes on the above graph. 1) 0.5 secs seems to lie in the first linear section of the graph, so we get the two endpoints of that segment and find the slope. (0,-4) and (1,9) Slope = (9- -4)/(1 - 0) = 13 m/s 2) 6.5 secs lies on the segment between t = 5 and t = 8, so again we can find the endpoints and calculate the slope: (5,4) and (8,-7) Slope = (-7 - 5)/(8-5) = -12/3 = -4 m/s 3) To find the average velocity between t = 0 and t = 3, we take those two points and find the slope between them: (0, -4) and (3, 4) Slope = (4 - -4)/(3 - 0) = 8/3 m/s 4) For the average velocity over the whole interval, we take the two endpoints and find the slope between them: (0, -4) and (9, 1) Slope = (1 - -4)/(9- 0) = 5/9 m/s

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