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6. A particle is moving in the positive direction along the x axis. The graph below shows its velocity, v(t), in feet per second, after t seconds. Include correct units in your answers. a. Find the average acceleration of the particle over the time interval t = 2s to t = 9s. b. What is the acceleration of the car at t = 4s? c. What is the difference between the average acceleration and acceleration? Use both a physical explanation and a graphical explanation. d. Draw the graph of the acceleration function.

          6. A particle is moving in the positive direction along the x axis. The graph below shows its velocity, v(t), in feet per second, after t seconds. Include correct units in your answers.
a. Find the average acceleration of the particle over the time interval t = 2s to t = 9s.
b. What is the acceleration of the car at t = 4s?
c. What is the difference between the average acceleration and acceleration? Use both a physical explanation and a graphical explanation.
d. Draw the graph of the acceleration function.
        
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6. A particle is moving in the positive direction along the x axis. The graph below shows its velocity, v(t), in feet per second, after t seconds. Include correct units in your answers.
a. Find the average acceleration of the particle over the time interval t = 2s to t = 9s.
b. What is the acceleration of the car at t = 4s?
c. What is the difference between the average acceleration and acceleration? Use both a physical explanation and a graphical explanation.
d. Draw the graph of the acceleration function.

Added by James S.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The graph below shows the velocity of a particle moving in the positive direction along the X-axis. Include correct units in your answers: V(t), in feet per second, after t seconds. Find the average acceleration of the particle over the time interval t = 2s to t = 9s. What is the acceleration of the particle at t = 45? What is the difference between the average acceleration and acceleration? Use both an explanation and a physical graphical explanation. Draw the graph of the acceleration function.
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Transcript

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00:01 So for this problem, we're given the graph of velocity, we want to find average acceleration from two seconds to nine seconds.
00:10 So to do this, we look at the velocity at two seconds, which we see is zero.
00:16 So it's going to be v of average acceleration will be v of 9 minus v of 2.
00:21 That's our delta v over the delta t.
00:24 So that's going to be 9 minus 2.
00:27 So at 2, our velocity is 0, but at 9, our velocity.
00:31 Is 10.
00:33 So we're going to have 10 minus 0 over 9 minus 2, which is 7.
00:37 So we'd get 10 7th meters per second square.
00:40 Then we want to know the acceleration of the car at four seconds exactly.
00:46 Well, that's going to be the slope.
00:48 So we need to look at points surrounding at this point.
00:54 We see that if we look a little bit below, so say 3 .5, we have the point 3 .5 and looks to be about 7...
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