Velocity and Acceleration for a Trig equation

A particle moves in a straight line along the x-axis so that its position, x(t), at time t seconds, t≥0, is given by x=sin(pi.t^2)

a) Find expressions for the velocity and acceleration of the particle at time t

b) Find the times for which the particle is stationary

If anyone could help with this question, that would be great

Re: Velocity and Acceleration for a Trig equation

Do you know the definitions of velocity and acceleration?

Re: Velocity and Acceleration for a Trig equation

I think velocity will just be the derivative, however I have forgotten what acceleration will be

Re: Velocity and Acceleration for a Trig equation

Quote:

Originally Posted by

**gbooker** I think velocity will just be the derivative, however I have forgotten what acceleration will be

Acceleration is the second derivative of displacement (or the first derivative of velocity)

Re: Velocity and Acceleration for a Trig equation

ok so as a result of that the derivative (velocity) = (cos.pi.x^2). (2x.pi)

so does that mean for part b is it just solve for when velocity=0?

Re: Velocity and Acceleration for a Trig equation

Quote:

Originally Posted by

**gbooker** ok so as a result of that the derivative (velocity) = (cos.pi.x^2). (2x.pi)

so does that mean for part b is it just solve for when velocity=0?

yes, $\displaystyle v(t) = 2\pi t \cdot \cos(\pi t^2) = 0$

solve for those values of $\displaystyle t \ge 0$ that make the velocity zero.