Question 1

A car moves along a straight road such that its position as a function of time is given by $x(t) = 4t^2 + 2t + 1$ (where $x$ is in meters and $t$ in seconds). What is the instantaneous velocity of the car at $t = 3$ s?

Accepted Answer

$v = 26$ m/s

Question 2

A runner completes a 100 m dash in 10 s, starting from rest and finishing at a constant speed. What is the runner's average velocity during the race?

Accepted Answer

$v_{	ext{avg}} = 10$ m/s

Question 3

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

Accepted Answer

Velocity is a vector and can be negative, while speed is always positive.

Question 4

A ball is thrown straight up with an initial velocity of $20$ m/s. Ignoring air resistance, what is the velocity of the ball when it returns to its starting point?

Accepted Answer

$-20$ m/s

Question 5

A particle moves along the x-axis. Its velocity-time graph is a straight line with a positive slope. What can you say about the particle's acceleration?

Accepted Answer

The acceleration is constant and positive.

Question 6

A stone is dropped from rest from a bridge and falls freely under gravity. How far does it fall in the first 2 seconds? (Take $g = 9.8$ m/s$^2$)

Accepted Answer

$19.6$ m

Question 7

Which equation correctly relates displacement, initial velocity, acceleration, and time for motion with constant acceleration?

Accepted Answer

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

Question 8

A car accelerates from $10$ m/s to $30$ m/s in $5$ seconds. What is its average acceleration?

Accepted Answer

$4$ m/s^2$

Question 9

A position-time graph of a particle is a straight line with a negative slope. What does this indicate about the particle's motion?

Accepted Answer

The particle is moving in the negative x-direction with constant velocity.

Question 10

A cyclist travels 40 km east in 2 hours, then 30 km west in 1 hour. What is the cyclist's average velocity for the entire trip?

Accepted Answer

$3.33$ km/h east

Question 11

If the velocity of a particle is given by $v(t) = 3t^2$, what is the acceleration at $t = 2$ s?

Accepted Answer

$a = 12$ m/s$^2$

Question 12

A car moves with a constant acceleration of $2$ m/s$^2$. If its initial velocity is $5$ m/s, what is its velocity after $4$ seconds?

Accepted Answer

$13$ m/s

Question 13

A ball is thrown vertically upward with a speed of $15$ m/s. How long does it take to reach its highest point? (Take $g = 9.8$ m/s$^2$)

Accepted Answer

$1.53$ s

Question 14

Which of the following best describes the acceleration of a freely falling object near Earth's surface (ignoring air resistance)?

Accepted Answer

It is constant and directed downward.

Question 15

A particle's velocity changes from $-5$ m/s to $+5$ m/s in $2$ seconds. What is its average acceleration?

Accepted Answer

$5$ m/s$^2$

Question 16

A car travels at $20$ m/s for $5$ seconds, then accelerates uniformly to $40$ m/s over the next $5$ seconds. What is the total distance traveled in $10$ seconds?

Accepted Answer

$300$ m

Question 17

Which of the following is the correct integral expression for position as a function of time when acceleration is not constant?

Accepted Answer

$x = x_0 + \int v_x dt$

Question 18

A position-time graph has a tangent with zero slope at $t = 2$ s. What does this indicate about the particle's motion at that instant?

Accepted Answer

The particle is instantaneously at rest.

Question 19

A car's velocity-time graph is a horizontal line at $v = 10$ m/s. What is the car's acceleration?

Accepted Answer

$0$ m/s^2$

Chapter 02

Study Guide - Practice Questions

Study Guide - Flashcards