Show that if the speed of a particle along a curve is constant, then the velocity and acceleration vectors are orthogonal.

Suppose that x is a $C^2$ path with nonzero velocity. Show that x has constant speed if and only if its velocity and acceleration vectors are always perpendicular to one another.

Explain how a particle can be accelerating even though its speed is constant.

Describe how the mass of a gas particle affects its rate of effusion and diffusion.

The speed of a particle at t = a is given by the value of the velocity at t = a. Justify your answer.

How far from a very small $100-\mathrm{~kg}$ ball would a particle have to be placed so that the ball pulled on the particle just as hard as the earth does? Is it reasonable that you could actually set up this as an experiment? Why?

A particle moves according to a law of motion s=f(t), t \geqslant 0, where t is measured in seconds and s in feet.

Draw a diagram like Figure 2 to illustrate the motion of the particle.

$$f(t)=\cos (\pi t / 4)$$

Identify the unknown nuclide or particle (X).

$$X \rightarrow_{28}^{65} \mathrm{Ni}+\gamma$$

Sketch the graph of the height of a particle against time if velocity is positive and acceleration is negative.

If the kinetic energy of a particle is doubled, by what factor has its speed increased?

If the speed of a particle is halved, by what factor does its kinetic energy change?

Describe the structure of a typical atom. Identify where each subatomic particle is located.

If the kinetic energy of a particle is tripled, by what factor has its speed increased?

If the speed of a particle triples, by what factor does its kinetic energy increase?