Consider the motion of a particle that experiences a variable acceleration given
ID: 1999838 • Letter: C
Question
Consider the motion of a particle that experiences a variable acceleration given by ax = a0 + bt, where a0 and b are constants and x = x0 and vx = v0 at t = 0. (Use the following as necessary: a0, v0, x0, b, and t. )
(a) Find the instantaneous velocity as a function of time.
vx = _______________________
(b) Find the position as a function of time.
x = _________________________
(c) Find the average velocity for the time interval with an initial time of zero and arbitrary final time t.
vx = __________________________________
(d) Compare the average of the initial and final velocities to your answer to Part (c). Are these two averages equal?
(Yes) or ( No)?
Explanation / Answer
a) Vx= adt =integ(a0+bt)dt=a0t+0.5bt^2+c1 by substuting at t=0 then c1=v0
b) X=vxdt =intega0tdt +0.5bt^2dt +integc1dt +c2= 0.5t^2 +(bt^3)/6+v0t at t=0 c2=x0
c) V averge = x/(0+t) =x/t=0.5a0t+bt^2/6+v0+x0/t
d) Yes.