A particle moves along the x-axis in such a way that its acceleration at time t for t>= 0 is given by a(t)=4cos(2t). At time t=0, the velocity of the particle is v(0)=1 and its position is x(0)=0.(adsbygoogle = window.adsbygoogle || []).push({});

a. Write an equation for the velocity of v(t) of the particle.

b. Write an equation for the position x(t) of the particle.

c. For what values of t, 0<=t<=pi, is the particle at rest

-------------------------------------

a = dv/dt

4*cos(2t) = dv/dt

v = Integral[4*cos(2t) dt] + C

v = 2 * sin(2t) + C

t = 0 -> v = 1.

1 = 2 * sin(2*0) + C

C = 1

v(t) = 2 * sin(2t) + 1

How would I go about x(t)?

And for c. 2sin(2t)+1=0 sin2t=-1/2

arcsin2t=(1/2)

t=-.261799?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Equations (calc)

**Physics Forums | Science Articles, Homework Help, Discussion**