Q: A car moves with constant velocity $v_0$ for $5$ seconds, then accelerates at $2$ m/s$^2$ for $3$ seconds. What is its total displacement?

$5v_0 + 3v_0 + \frac{1}{2} \times 2 \times 3^2 = 5v_0 + 3v_0 + 9 = 8v_0 + 9$ m

Q: A drag racer’s velocity increases linearly from $0$ to $12$ m/s in $3$ seconds. What is the displacement during this time?

$\Delta x = \frac{1}{2} \times 12 \times 3 = 18$ m

Question 1

A car's velocity as a function of time is given by $v(t) = 4t$ m/s, where $t$ is in seconds. If the car starts at position $s_i = 0$ m at $t_i = 0$ s, what is its position at $t_f = 3$ s?

Accepted Answer

$s_f = 18$ m

Question 2

Which of the following best describes the graphical interpretation of the integral $\int_{t_i}^{t_f} v_s \, dt$?

Accepted Answer

It is the area under the velocity curve between $t_i$ and $t_f$.

Question 3

A ball rolls up a ramp and then down. Which acceleration graph correctly represents its motion?

Accepted Answer

Acceleration is constant and positive while on the ramp, zero on the horizontal.

Question 4

A springbok accelerates at $35$ m/s$^2$ for $0.70$ s as it leaps upward. What is its final velocity at the end of the acceleration phase?

Accepted Answer

$v_f = 24.5$ m/s

Question 5

An air balloon travels upward at a constant speed of $8$ m/s. A passenger drops a sandbag over the side. What is the initial velocity of the sandbag immediately after release?

Accepted Answer

$8$ m/s$\,$$\uparrow$

Question 6

Which equation gives the displacement $\Delta x$ for an object with constant acceleration $a$ and initial velocity $v_0$ over time interval $\Delta t$?

Accepted Answer

$\Delta x = v_0 \Delta t + \frac{1}{2} a \Delta t^2$

Question 7

A hiker walks $3$ miles east, then $4$ miles north. What is the magnitude of the hiker's net displacement?

Accepted Answer

$5$ miles

Question 8

A vector $\vec{A}$ has components $A_x = 3$ and $A_y = 4$. What is the magnitude of $\vec{A}$?

Accepted Answer

$5$

Question 9

If a vector $\vec{B}$ has a magnitude of $10$ units and points $30^\circ$ above the x-axis, what is its y-component?

Accepted Answer

$B_y = 10 \sin 30^\circ = 5$

Question 10

Which statement is true about the signs of velocity and acceleration for an object speeding up?

Accepted Answer

Velocity and acceleration have the same sign.

Question 11

A bird flies $100$ m due east, then $50$ m northwest ($45^\circ$ north of west). What is the x-component of its net displacement?

Accepted Answer

$100 - 50 \cos 45^\circ = 64.6$ m

Question 12

On an inclined plane tilted at angle $	heta$, the acceleration along the plane is given by:

Accepted Answer

$a = g \sin 	heta$

Question 13

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 14

If $v(t)$ is the velocity function, which formula gives the instantaneous acceleration $a(t)$?

Accepted Answer

$a(t) = \frac{dv}{dt}$

Question 15

A vector $\vec{A}$ is decomposed into components $A_x$ and $A_y$. Which equation correctly relates the magnitude of $\vec{A}$ to its components?

Accepted Answer

$|\vec{A}| = \sqrt{A_x^2 + A_y^2}$

Question 16

A car moves with constant velocity $v_0$ for $5$ seconds, then accelerates at $2$ m/s$^2$ for $3$ seconds. What is its total displacement?

Accepted Answer

$5v_0 + 3v_0 + \frac{1}{2} 	imes 2 	imes 3^2 = 5v_0 + 3v_0 + 9 = 8v_0 + 9$ m

Question 17

Which of the following is the correct vector sum for three vectors $\vec{A}$, $\vec{B}$, and $\vec{C}$?

Accepted Answer

$\vec{A} + \vec{B} + \vec{C}$

Question 18

If a vector $\vec{D}$ points in the negative y-direction and has a magnitude of $5$, how is it written using unit vectors?

Accepted Answer

$\vec{D} = -5 \vec{j}$

Question 19

A drag racer’s velocity increases linearly from $0$ to $12$ m/s in $3$ seconds. What is the displacement during this time?

Accepted Answer

$\Delta x = \frac{1}{2} 	imes 12 	imes 3 = 18$ m

Kinematics: Position, Velocity, Acceleration, and Vectors

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