A particle starts from the origin at t = 0 and moves along the positive x axis.

Question

A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in the figure; the v-axis scale is set by vs = 8.0 m/s. (a) What is the coordinate of the particle at t = 5.0 s? (b) What is the velocity of the particle at t = 5.0 s? (c) What is the acceleration of the particle at t = 5.0 s? (d) What is the average velocity of the particle between t = 1.0 s and t = 5.0 s? (e) What is the average acceleration of the particle between t = 1.0 s and t = 5.0 s?

Explanation / Answer

a)
at t = 5

area is given as

A = (0.5) (2) (16) + (4 - 2) (16 - 0) + (0.5) (8) (5 - 4) + (8) (1) = 60

so coordiate at t = 5 is (60, 0)

b)

v = (8 - 16)/(5 - 4) = - 8 m/s

c)

a = 0

since the velocity is constant at t = 5

d)

Vavg = (8 - 0)/(5 - 1) = 2 m/s

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