Q: If a car travels 50 m east in 24 s, then 50 m west in 48 s, what is the average speed for the entire trip?

$$\text{Average speed} = \dfrac{50 + 50}{72} = 1.39\,\mathrm{m/s}$$

Question 1

A car moves from an initial position $$\vec{x}_i = 2\,\mathrm{m} to a $$final position $$\vec{x}_f = 10\,\mathrm{m}$$ along the x-axis. What is the displacement of the car?

Accepted Answer

$$\Delta \vec{x} = 8\,\mathrm{m}$$

Question 2

A runner completes a 50 m race in 24 s, then immediately returns to the starting point in another 48 s. What is the average velocity for the entire trip?

Accepted Answer

$$\vec{v}_{avg} = 0\,\mathrm{m/s}$$

Question 3

Which of the following best describes the difference between distance and displacement?

Accepted Answer

Distance is a scalar and measures the total path length; displacement is a vector and measures the straight-line change in position.

Question 4

Given the position-time graph $$x(t)$$ shown, what is the velocity at $$t = 2\,\mathrm{s} if$$ $$x(2) = 0\,\mathrm{m}$$ and $$x(1) = -2\,\mathrm{m}$$?

Accepted Answer

$$v = \dfrac{0 - (-2)}{2 - 1} = 2\,\mathrm{m/s}$$

Question 5

A cat starts from rest and accelerates uniformly to $$20.11\,\mathrm{m/s} in$$ $$2\,\mathrm{s}. $$What is the acceleration?

Accepted Answer

$$a_x = \dfrac{20.11 - 0}{2} = 10.055\,\mathrm{m/s^2$}$$

Question 6

A ball is thrown vertically upward from a roof with $$v_{oy} = +5\,\mathrm{m/s}$$ from $$y_0 = +40$$\,\mathrm{m}$$. What is the acceleration acting on the ball?

Accepted Answer

$$a_y = -9.8\,\mathrm{m/s^2$}$$

Question 7

A truck moves with velocity $$\vec{v}_1 at$$ $$t_1$$ and $$\vec{v}_2 at$$ $$t_2$$, both to the left, and the acceleration $$\vec{a}$$ points to the right. What happens to the truck's speed?

Accepted Answer

The truck slows down.

Question 8

If a car travels 50 m east in 24 s, then 50 m west in 48 s, what is the average speed for the entire trip?

Accepted Answer

$$	ext{Average speed} = \dfrac{50 + 50}{72} = 1.39\,\mathrm{m/s}$$

Question 9

Which of the following is true about the velocity vector?

Accepted Answer

It points in the direction of displacement.

Question 10

A position-time graph shows a curve that gets steeper with time. What does this indicate about the object's motion?

Accepted Answer

The object is accelerating.

Question 11

A truck starts at $$x_0 = 0$ with v_0$ = 0$$ and accelerates at $$a_x = 2\,\mathrm{m/s^2$}$$ for $$t = 3\,\mathrm{s}. $$What is its position at $$t = 3\,\mathrm{s}$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \dfrac{1}{2} a_x t^2$ = 0 + 0 + \dfrac{1}{2} 	imes 2 	imes 9 = 9\,\mathrm{m}$$

Question 12

If the velocity-time graph is a straight line with positive slope, what does this indicate?

Accepted Answer

The object has constant positive acceleration.

Question 13

A ball is thrown upward from a roof. At the top of its path, what is its velocity?

Accepted Answer

$$v_{top} = 0$$

Question 14

A car moves in three stages: Part 1 ($$a_1 = 2$$\,\mathrm{$$m/s^2$$}$$, $$\Delta $$t_1 = 2$$\,\mathrm{s}$$), Part 2 (a_2$ = 0$$, $$\Delta t_2$ = 3\,\mathrm{s}$$), Part 3 ($$a_3 = -1$$\,\mathrm{$$m/s^2$$}$$, $$\Delta $$t_3 = 4$$\,\mathrm{s}$$). What is the total displacement?

Accepted Answer

$$\Delta x_{total} = \dfrac{1}{2} a_1$ t_1$^2 + v_{1,final} t_2$ + v_{2,final} t_3$ + \dfrac{1}{2} a_3$ t_3$^2$$

Question 15

Two objects start at different positions and move with different accelerations. Which equation would you use to find when they meet?

Accepted Answer

$$(x_{0,1} + v_{0,1} t + \dfrac{1}{2} a_{1} t^2$) = (x_{0,2} + v_{0,2} t + \dfrac{1}{2} a_{2} t^2$)$$

Motion Along a Straight Line: Displacement, Velocity, and Acceleration

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