Question

.4.5 프 Assigned Media A body moves on a coordinate line such that it has a position s fon the interval 1sts2 with s in meters and t in seconds. a position s f) on the interval a Find the body's displacement and average velocity for the given time interval. b. Find the body's speed and acceleration at the endpoints of the interval c. When, if ever, during the interval does the body change direction?

Answer 1

(a) The body's displacement is given by substituting the values in the function for t=1 and t=2

s(2) _ s(1)ーアー21-112--]-(1-1)-(4-2)-2

Hence the displacement is equal to -2m

average velocity- 2-1

Hence the average velocity is equal to -2 m/s

(b)

d,4 22

r(2) =-+ 1 + 0.5 =-0.5 23 22

Speed is equal to the modulus of the velocity at the end point, hence the body's speed is equal to 0.5 m/s

d-8 224 4 dlt

24 4 1.5-0.5-1m/s2 a(2)

c) The direction will be changed when the velocity vector becomes zero

1 0 3t

8

t' = 4, t =-2.2

Hence the direction will be changed at time equal to 2

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