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 = 4.0 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)the coordinate of the particle at t = 5.0 s is the areaunder the strokes from 0 --> 5 x=(2+6)*16/2 -1*8*1/2=68 m (b) the velocity of the particle at t = 5.0s: v=8 m/s (c)the acceleration of the particle at t= 5.0 s from t=4s to 6s the acceleration of the particle is constant=-16/2=-8 m/s2 (d) the averagevelocity of the particle between t = 1.0 s and t= 5.0 s average velocity=total distance traveled /total time=[(2+4)*8/2+8*4]/4=14 m/s (e)the average acceleration ofthe particle between t = 1.0 s and t = 5.0 s a=(8*1s +8*1s)/4 =4 m/s2

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