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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