Q: A student walks $$d_1$$ meters east, $$d_2$$ meters north, and $$d_3$$ meters at an angle $$\phi$$ south of west. Which equation gives the $$x-$$component of the total displacement?

$$S_x = d_1$ + d_2$ \cos \theta - d_3$ \cos \phi$$

Question 1

A drone flies in a straight line at constant speed $$v_d$$ toward a stationary person. When the drone passes overhead, the person starts running in the same direction as the drone at a constant acceleration $$a_r. If $$the drone accelerates at a rate of $$a_d$$, which equation best expresses the time $$t$$ when the person will catch up to the drone?

Accepted Answer

$$t = \frac{2v_d}{a_r}$$

Question 2

Which of the following best describes the difference between displacement and distance for a moving object?

Accepted Answer

Displacement is the shortest path between two points, while distance is the total length traveled.

Question 3

A student walks $$d_1$$ meters east, $$d_2$$ meters north, and $$d_3$$ meters at an angle $$\phi$$ south of west. Which equation gives the $$x-$$component of the total displacement?

Accepted Answer

$$S_x = d_1$ + d_2$ \cos 	heta - d_3$ \cos \phi$$

Question 4

If two objects have the same velocity at a certain instant, which of the following must be true?

Accepted Answer

They are moving in the same direction with the same speed at that instant.

Question 5

Given the kinematic equation $$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$, which variable represents the initial position?

Accepted Answer

$$x_0$$

Question 6

A car accelerates from rest at $$2 	ext{ m/s}^2$$ for $$5$$ seconds. What is its final velocity?

Accepted Answer

$$v = 10 	ext{ m/s}$$

Question 7

Which of the following is a correct vector equation for the total displacement $$\vec{s}$$ after walking $$d_1$$ east, $$d_2$$ north, and $$d_3 at $$angle $$\phi$$ south of west?

Accepted Answer

$$\vec{s} = d_1$ \hat{i} + d_2$ \hat{j} - d_3$ (\cos \phi \hat{i} + \sin \phi \hat{j})$$

Question 8

A ball is thrown vertically upward with initial velocity $$v_0. $$What is its velocity after time $$t$$ under gravity $$g$$?

Accepted Answer

$$v = v_0$ - gt$$

Question 9

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity.

Question 10

A runner moves with constant acceleration $$a$$ from rest. Which equation gives the distance covered after time $$t$$?

Accepted Answer

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

Question 11

Which of the following is NOT a scalar quantity?

Accepted Answer

Displacement

Question 12

A student walks $$4 m $$east, $$3 m $$north, and $$5 m $$west. What is the magnitude of the net displacement?

Accepted Answer

$$\sqrt{(4-5)^2$ + 3^2$} = \sqrt{1^2$ + 3^2$} = \sqrt{10} m$$

Question 13

Which kinematic equation is most appropriate for finding the time it takes an object to reach a certain displacement under constant acceleration?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 14

A car travels $$100 m $$north, then $$100 m $$east. What is the magnitude of its displacement?

Accepted Answer

$$\sqrt{100^2$ + 100^2$} = 141.4 m$$

Question 15

Which of the following best describes the velocity of an object moving in a circle at constant speed?

Accepted Answer

The velocity is constant in magnitude but changes direction.

Question 16

A student walks $$d_1$$ meters east, $$d_2$$ meters north, and $$d_3$$ meters at an angle $$	heta$$ west of north. Which equation gives the $$y-$$component of the total displacement?

Accepted Answer

$$S_y = d_2$ + d_3$ \cos 	heta$$

Question 17

Which of the following is true about the acceleration of an object moving with constant velocity?

Accepted Answer

The acceleration is zero.

Question 18

A runner accelerates at $$3 	ext{ m/s}^2$$ for $$4$$ seconds from rest. What is the total distance covered?

Accepted Answer

$$d = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 3 	imes 16 = 24 m$$

Question 19

Which of the following is a correct statement about vector addition?

Accepted Answer

Vectors are added by summing their components.

Kinematics and Vectors: Study Notes for Physics 10310 Quiz #1

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