Question 1

A particle's position vector is given by $$\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}. If at $$time $$t = 0$$ the particle is at $$(2, 3, 4)$$ and at $$t = 5 s it is at$$ $$(7, 1, 6)$$, what is the displacement vector $$\Delta \vec{r}$$?

Accepted Answer

$$\Delta \vec{r} = 5\hat{i} - 2\hat{j} + 2\hat{k}$$

Question 2

The average velocity vector $$\vec{v}_{av}$$ between two points is defined as:

Accepted Answer

$$\vec{v}_{av} = \frac{\vec{r}_2 - \vec{r}_1}{t_2$ - t_1$}$$

Question 3

A dragster moves from $$x_1 = 19$ m at t_1$ = 1.0 s to$$ $$x_2 = 277$ m at t_2$ = 4.0 s. $$What is its average velocity?

Accepted Answer

$$v_{av} = 86 m/s$$

Question 4

The instantaneous velocity of a particle whose position vector is $$\vec{r} = a\cos(\omega t)\hat{i} + b\sin(\omega t)\hat{j} + ct^2$\hat{k} is$$:

Accepted Answer

$$\vec{v} = -a\omega\sin(\omega t)\hat{i} + b\omega\cos(\omega t)\hat{j} + 2ct\hat{k}$$

Question 5

On an $$x$$-$$t$$ graph, the instantaneous velocity at any point is:

Accepted Answer

The slope of the tangent to the curve at that point

Question 6

A particle moves along a path such that its velocity vector is always tangent to the path. Which component of acceleration changes the speed?

Accepted Answer

The component tangent to the path

Question 7

For motion with constant acceleration, which equation correctly relates displacement, initial velocity, and acceleration?

Accepted Answer

$$x = x_0$ + v$$_{0x}$$t + \frac{1}{2}a_xt^2$

Question 8

A projectile is launched with initial velocity $$v_0 at $$angle $$\$$alpha_0$$ above the horizontal. What is the vertical velocity at time t$?

Accepted Answer

$$v_y = v_0$\sin\$$alpha_0$$ - gt$$

Question 9

You throw a ball from a window 8.0 m above the ground at $$10.0 m/s$$, $$20^\circ$$ below the horizontal. Ignoring air resistance, which equation gives the time $$t$$ when the ball hits the ground?

Accepted Answer

$$t = \frac{v_0$\sin\$$alpha_0$$ + \sqrt{(v_0$\sin\$$alpha_0$$)^2 - 2g y$$}}{g}$

Question 10

In uniform circular motion, the radial acceleration $$a_{rad} is $$given by:

Accepted Answer

$$a_{rad} = \frac{v^2$}{R}$$

Question 11

A car rounds a banked curve of radius $$R at $$speed $$v. If $$the curve is perfectly banked for this speed, what is the direction of the net force acting on the car?

Accepted Answer

Toward the center of the curve

Question 12

A centrifuge spins at angular speed $$\omega. If $$the radius is $$R$$, what is the speed $$v of a $$sample in the centrifuge?

Accepted Answer

$$v = R\omega$$

Question 13

A cyclist moves east at $$10 m/s. A $$train moves north at $$20 m/s. $$What is the velocity of a passenger relative to the cyclist?

Accepted Answer

$$\vec{v}_{P/A} = 10\hat{i} + 20\hat{j}$$

Question 14

An airplane heads north at $$240 km/h. $$There is a $$100 km/h $$wind from west to east. What is the airplane's velocity relative to the earth?

Accepted Answer

$$\vec{v}_{PE} = 240\hat{j} + 100\hat{i}$$

Question 15

A jet plane has velocity components $$v_x = 90 m/s$$, $$v_y = 110 m/s at$$ $$t_1 = 0$ and v_x = -170$ m/s, v_y = 40$ m/s at t_2$ = 30 s. $$What is the average acceleration vector?

Accepted Answer

$$\vec{a}_{av} = \frac{(-170 - 90)\hat{i} + (40 - 110)\hat{j}}{30}$$

Question 16

For a particle moving in a circle, which statement is true about the direction of velocity and acceleration in uniform circular motion?

Accepted Answer

Velocity is tangent to the circle, acceleration is radial and points toward the center

Question 17

A motorist travels at constant speed $$v = 15 m/s. A $$police officer starts pursuit with constant acceleration $$a = 3.0 m/s$^2. $$How long does it take for the officer to catch up?

Accepted Answer

$$t = \frac{2v}{a}$$

Question 18

In projectile motion, what is the acceleration at the top of the trajectory?

Accepted Answer

$$a_y = -g$$, $$a_x = 0$$

Motion, Kinematics, and Vectors: Study Notes for College Physics

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