1) The position of an object moving along a straight line is given by x(t) = -3.

Question

1) The position of an object moving along a straight line is given by x(t) = -3.0t^3 + 2.0t^3 - 1.0t, where x is in meters, t > or equal 0, t is in seconds.

a) The average acceleration between t = 0 and t = 4.0 s is ________

b) The instantaneous acceleration at t = 1.0 is ________

c) Is this particle moving with a constant acceleration?  _____ Why?  ______

2) The position of a particle in meter is given by x(t) = 1.0t^3 + 1.0t^2 + 1.0t - 10, where the time t is in seconds and t > or equal 0. The acceleration of the particle is:

a)constant in +x direction

b)constant in -x direction

c)non-constant in +x direction

d)non-constant in -x direction

e) non-constant in +x direction first then in -x direction

3) An object moving in the +x axis experiences an acceleration of 2.0 m/s^2. This means the object is:

a)traveling at 2.0 m in every second

b)traveling at 2.0 m/s in every second

c) changing its velocity by 2.0 m/s

d) increasing its velocity by 2.0 m/s in every second

Explanation / Answer

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

v = dx/dt = -9t^2 + 4t

a) at t1 = 0, v1 = 0
   at t2 = 4s, v2 = -128 m/s
a = (v2-v1)/(t2-t1) = -32 m/s^2

b) a = dv/dt = -18*t +4

at t=1s, a = -18+4 = -14 m/s^2

c) no. it dpends on time


2)

c)non-constant in +x direction

3)
d) increasing its velocity by 2.0 m/s in every second

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