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?

A particle moves along a horizontal line so that its coordinate at time t is $x=\sqrt{b^2+c^2 t^2}, t \geqslant 0$, where b and c are positive constants.

Show that the particle always moves in the positive direction.

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.

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

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

The position function of a particle moving along the $x$-axis is

$$\begin{aligned} &x(t)=t^2-3 t+2 \\ &\text { for }-\infty<t<\infty \end{aligned}$$

Find the open $t$-interval(s) in which the particle is moving to the left.

Is an electron a particle or a wave? Support your answer by citing some experimental results.

The function $s(t)$ describes the motion of a particle moving along a line. For each function
Find the velocity function of the particle at any time $t \geq 0$ \

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

What is the momentum (as a function of time) of a 5.0-kg particle moving with a velocity $\overrightarrow{\mathbf{v}}(t)=(2.0 \hat{\mathbf{i}}+4.0 t \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$ ? What is the net force acting on this particle?

Find the velocity, speed, and acceleration at time $t$ of the particle whose position is $\mathbf { r } ( t )$ . Describe the path of the particle. $\mathbf { r } = a \cos t \mathbf { i } + a \sin t \mathbf { j } + c t \mathbf { k }$

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. \

$$s(t)=t^3-20 t^2+128 t-280$$

Identify the unknown particle on the left side of the following reaction? $+ p \rightarrow \mathrm{n}+\mu+$

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

The velocity function, in feet per second, is given for a particle moving along a straight line. Find the total distance that the particle travels over the given interval.

$$v(t)=t^{3}-8t^{2}+15t, \ 0 \leq t \leq5$$