Q: A projectile is launched from the ground at an angle $$\theta$$ with initial speed $$v_0. $$Which equation gives the horizontal range (distance) of the projectile, assuming no air resistance?

$$R = \frac{v_0$^2 \sin(2\theta)}{g}$$

Q: A particle moves in three dimensions. Its average velocity between times $$t_1$$ and $$t_2 is $$given by:

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

Question 1

A car moves along a curved path at constant speed. Which component of acceleration is responsible for changing the direction of the car's velocity?

Accepted Answer

The perpendicular component of acceleration ($$a_{\perp})$$

Question 2

Given the position vector $$\vec{r}(t) = x(t)\hat{i} + y(t)\hat{j} + z(t)\hat{k}$$, what is the formula for the instantaneous velocity vector?

Accepted Answer

$$\vec{v}(t) = \frac{d\vec{r}(t)}{dt}$$

Question 3

A projectile is launched from the ground at an angle $$	heta$$ with initial speed $$v_0. $$Which equation gives the horizontal range (distance) of the projectile, assuming no air resistance?

Accepted Answer

$$R = \frac{v_0$^2 \sin(2	heta)}{g}$$

Question 4

The area under an acceleration-time ($$a_x vs$$ $$t) $$graph between $$t_1$$ and $$t_2$$ represents:

Accepted Answer

The net change in $$x-$$velocity ($$\Delta v_x) $$from $$t_1 to$$ $$t_2$$

Question 5

A particle moves in three dimensions. Its average velocity between times $$t_1$$ and $$t_2 is $$given by:

Accepted Answer

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

Question 6

If a particle's velocity vector is always tangent to its path, what does this imply about its motion?

Accepted Answer

The particle is moving along a curved path

Question 7

A fountain shoots water in a parabolic arc. Which type of motion best describes the water's trajectory?

Accepted Answer

Projectile motion

Question 8

A car rounds a curve and slows down. What happens to its instantaneous velocity?

Accepted Answer

Both the magnitude and direction of velocity change

Question 9

Which equation correctly expresses the displacement vector $$\Delta \vec{r}$$ between two points $$P_1$$ and $$P_2$$?

Accepted Answer

$$\Delta \vec{r} = \vec{r}_2 - \vec{r}_1$$

Question 10

A particle moves along a curved path at constant speed. At which points does the particle have zero acceleration?

Accepted Answer

At no points along the curved path

Question 11

If the acceleration vector is parallel to the velocity vector, what happens to the particle's motion?

Accepted Answer

The speed changes but the direction remains constant

Question 12

If the acceleration vector is perpendicular to the velocity vector, what happens to the particle's motion?

Accepted Answer

The direction changes but the speed remains constant

Question 13

A skier moves along a ski-jump ramp, speeding up from point A to E and slowing down after E. At point D, which direction does the acceleration vector point?

Accepted Answer

Toward the inside of the curve and opposite to the velocity

Question 14

Given $$\vec{v} = (3.0\ 	ext{m/s})\hat{j}$$ and $$\vec{a} = (0.5\ 	ext{m/s}^2)\hat{i} - (0.2\ 	ext{m/s}^2)\hat{j}$$, what is the magnitude of the acceleration?

Accepted Answer

$$\sqrt{(0.5)^2$ + (-0.2)^2$} = 0.54\ 	ext{m/s}^2$$

Question 15

A football is kicked and follows a parabolic trajectory. At the highest point, what is the vertical component of its velocity?

Accepted Answer

Zero

Question 16

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration can change the magnitude and/or direction of velocity

Question 17

A particle's velocity changes from $$\vec{v}_1 to$$ $$\vec{v}_2$$ over a time interval $$\Delta t. $$What is the average acceleration?

Accepted Answer

$$\vec{a}_{	ext{av}} = \frac{\vec{v}_2 - \vec{v}_1}{\Delta t}$$

Question 18

Which of the following best describes the motion of a particle with constant acceleration perpendicular to its velocity?

Accepted Answer

The particle moves in a circle at constant speed

Question 19

If the speed of a particle is increasing, what can be said about its acceleration?

Accepted Answer

Acceleration must have a component in the direction of velocity

Question 20

A particle moves in the $$xy-$$plane with velocity components $$v_x$$ and $$v_y. $$What is the magnitude of its velocity?

Accepted Answer

$$\sqrt{v_x^2$ + v_y^2$}$$

Motion in One, Two, and Three Dimensions: Kinematics and Acceleration

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