3. A particle\'s position is described by the equation x-2.0+1.5t-0.4f m. (a) Wh

Question

3. A particle's position is described by the equation x-2.0+1.5t-0.4f m. (a) Where does the particle start its motion at t0? (b) What is the particle's average velocity over the time interval 1-2.00 s to 3.50 s? (c) What is the equation that describes the particle's instantaneous velocity? (d) Find the values of the instantaneous velocity at t 0, 1.0, and 2.5 s. (e) At what time(s), if any, is the object at rest? (f) What is the equation that describes the particle's instantaneous acceleration? (g) Is the acceleration constant or variable with time? (h) Describe the motion of the particle.

Explanation / Answer

a)

at t = 0; x = 2m

b)

Vavg = X3.5 - X2 / (3.5 - 2) = |2.35 - 3.4| / 1.5 = 1.05/1.5 = 0.7 m/s

c)

v = dx/dt = 1.5 - 0.8t

d)

V0 = 1.5 m/s

V1 = 0.7 m/s

V2.5 = -0.5 m/s

e)

rest @ v = 0

1.5-0.8t = 0

t = 1.875 sec

f)

a = dv/dt = -0.08 m/s^2

g)

acceleration is constant.

h)

The motion is called uniform retardation (negative acceleration) motion

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