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

Guida di studio - Domande di pratica

Study guide - Flashcard