For \(x(t)=4t^2\), find \(v_x\) at \(t=3\,\mathrm{s}\).

For \(x(t)=5t-2\), find the instantaneous velocity.

For \(x(t)=2/t\), find \(v_x\) at \(t=1\,\mathrm{s}\).

For \(x(t)=t^3-6t\), find \(v_x\) at \(t=2\,\mathrm{s}\).

For \(x(t)=t^2-8t\), when is the particle momentarily at rest?

For \(x(t)=t^3-3t^2\), find the times when the particle is momentarily at rest.

If \(v_x=-7\,\mathrm{m\,s^{-1}}\), what is the speed?

For \(x(t)=-2t^2+12t\), find \(v_x\) at \(t=4\,\mathrm{s}\).

For \(x(t)=t^3\), find \(v_x\) at \(t=0\).

If \(v_x>0\), what is happening to \(x(t)\)?

What does instantaneous velocity represent on a position-time graph?

For \(x(t)=3t^2+2t+1\), find \(v_x(t)\).

Why are the units of \(dx/dt\) metres per second?

What is the difference between instantaneous velocity and speed?

For \(x(t)=t^2-4t\), during what time interval is the particle moving in the negative direction?

For \(x(t)=A\cos(\omega t)\), find \(v_x(t)\).

For \(x(t)=10-3t\), find the velocity and state the direction of motion.

How is instantaneous velocity related to average velocity over smaller and smaller intervals?

If \(v_x=0\) at one instant, does the particle have to remain at rest?

A position-time graph has a local maximum at \(t=6\,\mathrm{s}\). What is \(v_x\) at that instant?

For \(x(t)=t^3-6t^2+9t\), find all times when the particle is instantaneously at rest and classify whether the position is locally increasing or decreasing between them.

A particle has \(x(t)=At^2+Bt+C\). Given \(x(0)=2\,\mathrm{m}\), \(x(1)=5\,\mathrm{m}\), and \(v_x(1)=7\,\mathrm{m\,s^{-1}}\), find \(x(t)\).