Q: Which equation correctly represents average velocity $v_{\text{avg}}$ over a time interval $\Delta t$?

$v_{\text{avg}} = \frac{\Delta x}{\Delta t}$

Question 1

Which of the following best defines displacement?

Accepted Answer

The change in position of an object, given by $\Delta x = x_{	ext{final}} - x_{	ext{initial}}$.

Question 2

A car travels 10 km east, then 5 km west. What is the car's displacement?

Accepted Answer

$5\ 	ext{km}$ east

Question 3

Which equation correctly represents average velocity $v_{	ext{avg}}$ over a time interval $\Delta t$?

Accepted Answer

$v_{	ext{avg}} = \frac{\Delta x}{\Delta t}$

Question 4

A runner moves with a constant velocity of $4\ 	ext{m/s}$ for $10\ 	ext{s}$. What is the displacement?

Accepted Answer

$40\ 	ext{m}$

Question 5

Which of the following statements about velocity and speed is correct?

Accepted Answer

Velocity is a vector, speed is a scalar.

Question 6

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

Accepted Answer

$10\ 	ext{m/s}$

Question 7

Which equation gives the position $x$ as a function of time $t$ for an object with constant acceleration $a$?

Accepted Answer

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

Question 8

A ball is thrown straight up with an initial velocity of $20\ 	ext{m/s}$. Neglecting air resistance, what is the maximum height reached? (Take $g = 9.8\ 	ext{m/s}^2$)

Accepted Answer

$20.4\ 	ext{m}$

Question 9

Which kinematic equation would you use to solve for the time it takes an object to reach a certain velocity under constant acceleration?

Accepted Answer

$v = v_0 + a t$

Question 10

A stone is dropped from rest from a height of $45\ 	ext{m}$. How long does it take to reach the ground? (Take $g = 9.8\ 	ext{m/s}^2$)

Accepted Answer

$3.03\ 	ext{s}$

Question 11

A car decelerates at $-6.0\ 	ext{m/s}^2$ from $25\ 	ext{m/s}$ to rest. What distance does it travel during this deceleration?

Accepted Answer

$52.1\ 	ext{m}$

Question 12

Which of the following is the correct graphical interpretation of velocity on a position vs. time graph?

Accepted Answer

The slope of the position vs. time graph at any point gives the velocity.

Question 13

A train travels the first half of a 100 km trip at $40\ 	ext{km/h}$ and the second half at $60\ 	ext{km/h}$. What is the average speed for the entire trip?

Accepted Answer

$48\ 	ext{km/h}$

Question 14

Which of the following is true for an object thrown vertically upward at $v_0$?

Accepted Answer

The time to reach maximum height equals the time to return to the original position.

Question 15

A car moves with a velocity given by $v(t) = 3t^2$. What is the acceleration at $t = 2\ 	ext{s}$?

Accepted Answer

$12\ 	ext{m/s}^2$

Question 16

Which of the following equations is NOT valid for constant acceleration?

Accepted Answer

$x = x_0 + v t^2$

Question 17

A ball is thrown downward with an initial velocity of $5\ 	ext{m/s}$ from a height of $20\ 	ext{m}$. How long does it take to hit the ground? (Take $g = 9.8\ 	ext{m/s}^2$)

Accepted Answer

$1.37\ 	ext{s}$

Question 18

If the velocity of an object is negative and its acceleration is positive, what happens to the object's speed?

Accepted Answer

It decreases.

Question 19

A car starts from rest and accelerates uniformly at $3\ 	ext{m/s}^2$ for $8\ 	ext{s}$. What is the total distance traveled?

Accepted Answer

$96\ 	ext{m}$

Question 20

Which of the following best describes instantaneous velocity?

Accepted Answer

The velocity of an object at a specific instant, given by $v = \frac{dx}{dt}$.

Motion in One Dimension: Kinematics and Applications

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