PROBLEMS: Please show ALL your work in NEAT & LOGICAL steps. Do not forget UNITS

Question

PROBLEMS: Please show ALL your work in NEAT & LOGICAL steps. Do not forget UNITS. 60 PTS 1· The velocity-time graph of the motion of a particle is shown below. a. Calculate the total displacement of the particle from 0 to 29 seconds. [6 p ts.] v (m/s) 34 32 30 28 26 24 20 1 8 16 14 12 10 6 4 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 t (s) b. Calculate the accelerations for the time intervals 0 to 6-s, 6-s to 14-s, and 17-s to 29-s. [6pts.] c. What is the average velocity of the particle from 0 to 29 seconds. 3pts.]

Explanation / Answer

a) Total displacement can be given by area under v-t graph. So

Displacement =Area= 1*6 + 0.5*6*30 +8*30 + 0.5*3*9 + 21*3 +. 5*21*12= 6+90+240+13.5+63+126

Displacement =538. 5 m.

b) Slope of v-t graph gives acceleration

Acceleration for 0 to 6 sec is a = 29/6 = 4.83 m/s2

Acceleration for 6 to 14 sec is a = 0/14 = 0 m/s2

Acceleration for 17 to 29sec is a = 21/12 = 1.75 m/s2

c) Average velocity is defined as ratio of total displacement to the total time so

Average velocity = 538.5/29 = 18.6 m/s.

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