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 = 5.0 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) Each rectangle on the graph represents 5m/s * 1s = 5 m.
For 0 s t 5 s
Mathematically, you can calculate the area under the acceleration portion, the coasting portion and the deceleration portion as follows:
s = (10m/s /2)2s + 10m/s*2s + (10+5)/2*1s = 37.5
with the same result.

(b) Read from the graph, v(5) = 5 m/s

(c) a = v / t = -10m/s / 2s = -5 m/s²

(d) Vavg = d / t = 37.5m / 5s = 7.5 m/s

(e) a_avg = v / t = 5m/s / 5s = 1 m/s²

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