The position of an object moving in a straight line is given by x = 2 t - 3 t 2

Question

The position of an object moving in a straight line is given by x = 2t - 3 t 2 + 2t 3, where x is in meters and t in seconds.

(a) What is the position of the object at t = 1s?
___m
What is the position of the object at t = 2?
___m
What is the position of the object at t = 3?
___m
What is the position of the object at t = 4 s?
___m

(b) What is the object's displacement between t = 0 and t = 4 s?
m

(c) What is the average velocity for the time interval from t = 2 s to t = 4 s?
m/s

(d) Graph x versus t for 0 t 4 s and indicate how the answer for (c) can be found on the graph. (Do this on paper. Your instructor may ask you to turn in this graph.)

Explanation / Answer

a)

here

x = 2 * t - 3 *t^2 + 2*t^3

at t= 1 sec

x = 2 * 1 - 3 *1 + 2 * 1

x = 1 m

at t= 2 sec

x = 2 * 2 - 3 * 4 + 2 * 8

x = 8 m

at t = 3 sec

x = 2 * 3 - 3 * 9 + 2 * 27

x = 33 m

then at t = 4 sec

x = 2 * 4 - 3 * 16 + 2 * 64

x = 88 m

b)

the displacement between t = 0 to t= 4 sec

d = 88 - 0 = 88 m

c)

average velocity = total distance travelled / total time

from t= 2sec to t = 4 sec

Vav = ( 87) / 2

Vav = 43.5 m/s

the average velocity form t= 2 sec to 4 sec is 43.5 m/s

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