GOAL Obtain average and instantaneous velocities from a graph. PROBLEM A train m
ID: 1660248 • Letter: G
Question
GOAL Obtain average and instantaneous velocities from a graph.
PROBLEM A train moves slowly along a straight portion of track according to the graph of position versus time in the left hand figure. (a) Find the average velocity for GOAL Obtain average and instantaneous velocities from a graph.
PROBLEM A train moves slowly along a straight portion of track according to the graph of position versus time in the left hand figure. (a) Find the average velocity for the total trip. (b) Find the average velocity during the first 4.00 s of motion. (c) Find the average velocity during the next 4.00 s of motion. (d) Find the instantaneous velocity at t = 2.00 s (e) Find the instantaneous velocity at t = 9.00 s.
STRATEGY The average velocities can be obtained by substituting the data into the definition. The instantaneous velocity at t = 2.00 s is the same as the average velocity at that point because the position vs. time graph is a straight line, indicating constant velocity. Finding the instantaneous velocity when t = 9.00 s requires sketching a line tangent to the curve at that point and finding its slope.
(d) Find the average and instantaneous velocity at t = 9.5 s.
x (m) (m) 2 0 0 + NO @ ® ON À o op 1 () $1 (s) 2 4 6 8 10 12 (a) 2 4 6 8 10 12 (b)Explanation / Answer
(A) average velocity = displacement / time
= 10 - 0 / 12
= 0.83 m/s
(B) during first 4 sec,
v = (4 - 0 ) / (4 - 0)
v = 1 m/s
(C) during next 4 sec,
v = (4 - 4) / (8 - 4) = 0
(d) instantenous velocity = slope of x vs t curve at that point
v = 4/4 = 1 m/s
(e) at t = 9 sec
v = (6.5 - 4) / (12 - 3)
v = 0.28 m/s
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