velocity and position of particle: a(t) = cos(t), t > 0

G

Guest

Guest
I have gotten so far and am stuck. I'd like to understand how to do this.

A particle, initially at rest, moves along the x-axis such that its acceleration at time t>0 is given by a(t)=cost. At the time t=0, its position is x=3.

(a.) find the velocity and position functions of the particle.
(b.) find the values of t for which the particle is at rest.

For velocity, I took the integral of the function.
Velocity is (sint+C), then for position I took the integral of velocity and got (-cost+Ct+C). C being a Constant.

Is that correct? And, that's where I get stuck and am unable to complete the problem. Thanks
 
Since the particle is initially at rest, you have \(\displaystyle v=0\)when \(\displaystyle t=0\). Then use the initial condition on position to evaluate the one constant left after your integration.
 
Sorry, still am not fully understanding. Do I have the right equations for Velocity and Position? And, I don't understand the question find the values(plural) of t for which the particle is at rest. What values are being referred to?
 
a(t) = cos(t)

v(t) = sin(t) + C
since v(0) = 0 ...
0 = sin(0) + C, therefore C = 0

v(t) = sin(t)

x(t) = -cos(t) + C
since x(0) = 3 ...
3 = -cos(0) + C, therefore C = 4

x(t) = -cos(t) + 4
 
You must log in or register to reply here.
Top