At time t equals or 0, the acceleration of a particle moving on the x axis is a(t)=t+sint.?

Question

At time t equals or > 0, the acceleration of a particle moving on the x axis is a(t)=t+sint.?

electrochika · Answer

at t=0 the velocity of the particle is -2. for what value t will the velocity of the particle be zero?

xishem · Answer

To find a velocity equation from an acceleration equation, you need to differentiate the acceleration equation with respect to t:
$$a'(t)=\cos(t)$$Now find the values for which this equation is equal to 0.
$$0=\cos(t)$$$$t=\pi/2, 3\pi/2$$

turingtest · Answer

$$v(t)=\int a(t)dt=\frac1 2t^2-\cos t+C$$$$v(0)=-1-2=C=-3$$$$v(t)=\frac1 2t^2-\cos t-3=0$$solve for t

anonymous · Answer

think this might be backwards
you are given acceleration and you want velocity

turingtest · Answer

Xishem has it backwards, yes

anonymous · Answer

what turing test said.

xishem · Answer

Yep.

electrochika · Answer

So t = - 2.917 and 2.917?

turingtest · Answer

yes, and I would imagine we want the positive answer here

electrochika · Answer

yeah we do

turingtest · Answer

oh yeah, positive only
it says so in the problem