Show that $E^2 - p^2c^2$ for a particle is invariant under Lorentz transformations.

In this exercise, the function $s(t)$ describes the motion of a particle moving along a line. For each function, identify the time(s) when the particle changes its direction.

$$s(t)=t^3-5 t^2+4 t$$

Identify the unknown nuclide or particle (X).

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

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

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.

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

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?

Why don't we notice energy quantization or particle wavelengths in everyday objects?

The function $\vec{p}=-3\left(2^t\right) \hat{i}+4 \cos (2 t) \hat{j}$ describes the position of a particle in the xy-plane. What is the speed and the magnitude of the acceleration vector of the particle when t=2?

(II) The momentum of a particle, in SI units, is given by $\overrightarrow{\mathbf{p}}=4.8 t^2 \hat{\mathbf{i}}-8.0 \hat{\mathbf{j}}-9.4 t \hat{\mathbf{k}}$. What is the force exerted on the particle as a function of time?

Make a graph of the kinetic energy versus momentum for a particle with zero rest mass.

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

If radium- 226 releases an alpha particle, what is the mass number of the isotope formed?