# Homework Help: Equations (calc)

1. Jan 8, 2004

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.
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?

2. Jan 9, 2004

### himanshu121

$$\frac{d^2x}{dt^2}=4\cos(2t)$$
$$\frac{dx}{dt}=\int 4\cos(2t)dt+c = 2sin2t+c$$
$$x=\int {2sin2t+c}dt+k$$