The figure below shows a graph of v_x versus t for the motion of a motorcyclist

Question

The figure below shows a graph of v_x versus t for the motion of a motorcyclist as he starts from rest and moves along the road in a straight line. (Assume all numbers in the figure are accurate to 2 significant figures.) Find the average acceleration for the time interval t = 0.0 to t = 3.0 s. Estimate the time at which the acceleration has its greatest positive value. What is the value of the acceleration at that instant? When is the acceleration zero? Estimate the maximum negative value of the acceleration. At what time does it occur? Draw position and acceleration graphs. These must be turned in on paper. Hint: This one is tricky... to approximate, redraw the velocity graph but with straight lines (one line from 0 to 5 seconds, a flat line from 5 to 7 seconds, a negatively sloped line from 7 to 10 seconds, and then a flat line from 10 to 12 seconds). Sketch the acceleration graph as piecewise constant, and then you can smooth out the transitions

Explanation / Answer

a) the speed changes from 0 to 4 in three seconds

Hence the average accelration = 4/3 = 1.33 ms-2

b) The instanneous accelerartion can be seen from the plot to be

Ai = 6-2/2= 2ms-2

c) acceleration is zero at t =6 and t >10

d) max negative is -2 ms-2 at 8 sec

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