6. Imagine that a group records the following position vs. time graph with a mot

Question

6. Imagine that a group records the following position vs. time graph with a motion detector. Position, meters 1.5 3.0 Time, seconds 0.5 1.0 2.0 2.5 Does the object ever have a positive acceleration? If so, describe the time interval or intervals and explain how you can tell. If not, explain why not a. b. Does the object ever have a negative acceleration? If so, describe the time interval or intervals and explain how you can tell. If not, explain why not. At approximately positive, negative, or zero? Explain. c. 1.7 s the object changes direction. Is the acceleration at this instant d. Calculate the velocity of the object at time 2.5 seconds. Be sure to show your work. e. Calculate the velocity of the object at time 1.0 second. Be sure to show your work

Explanation / Answer

(a)

Obect has positive acceleration from 0 to 1 s

(slope at any point in this period is +ve).

(b)

Obect has negative acceleration after 1 s.

(slope at any point in this period is -ve).

(c)

At t = 1.7 s

Slope on curve is along +x axis means velocity is 0 and acceleration will be negative

(d)

at t = 2.5 s

v = slope of curve at this point = (d2 - d1) / (t2 - t1)

v = (5 - 7) / (3 - 2)

v = -2 m/s

(e)

At t = 1 s

v = (d2 - d1) / (t2 - t1)

v = (6 - 5) / (1.1 - 0.8)

v = 3.3 m/s

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