Newton's First Law Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Newton's First Law.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

An object at rest stays at rest, and an object in motion continues moving at constant velocity in a straight line, unless acted upon by a net external force.

Things keep doing what they're doing unless something pushes or pulls them.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Newton's First Law asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to newton's first law but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Worked Examples

Example 1

easy

A book rests on a table. The weight of the book is

15 \text{ N}

downward. What is the normal force exerted by the table, and what is the net force on the book?

Book at rest on a table — balanced forces

Answer

N = 15 N upward, F_{net} = 0 N

First step

The book is at rest, so by Newton's first law, the net force must be zero.

Full solution

2
The normal force must balance the weight: $N = W = 15 N upward$
3
Net force: $F_{net} = N - W = 15 - 15 = 0 N$

Newton's first law states that an object at rest stays at rest unless acted on by a net external force. A book on a table is in equilibrium because the normal force balances gravity.

Example 2

medium

A hockey puck slides across a frictionless ice surface at

5 \text{ m/s}

. What is the puck's velocity after

10 \text{ seconds}

Example 3

easy

A passenger feels pushed backward when a bus accelerates forward. Which law explains this, and what is actually happening?

Example 4

medium

A bicyclist moves at constant velocity on level ground. The pedaling produces a forward force of

40 \text{ N}

. What is the magnitude of opposing (friction + drag) forces?

Bicyclist at constant velocity — opposing force equals pedaling force

Example 5

medium

An astronaut floating in the ISS pushes off a wall with

50 \text{ N}

for

0.5 \text{ s}

. Her mass is

60 \text{ kg}

. After her hand leaves the wall, describe her motion.

Example 6

medium

Why does a coin placed on top of a card on a glass fall straight into the glass when the card is flicked away quickly?

Example 7

hard

An object of mass

5 \text{ kg}

has three forces on it:

20 \text{ N}

east,

15 \text{ N}

30°

N of E, and

X

N west. For the object to remain at constant velocity, what is the magnitude of

X

and what is the additional force needed (if any)?

Example 8

hard

3 \text{ kg}

block hangs from two ropes: one horizontal, one at

60°

above horizontal. Find both tensions. Use

g = 9.8 \text{ m/s}^2

Block hanging from two ropes — find tensions T₁ and T₂

Example 9

hard

A car coasts down a hill of incline

5°

at constant speed. The car's mass is

1200 \text{ kg}

. What is the magnitude of the air drag plus rolling friction force? Use

g = 9.8 \text{ m/s}^2

Example 10

hard

A traffic light hangs at the center of a horizontal cable. The cable sags at angle

\theta = 10°

below horizontal on each side. The light's weight is

200 \text{ N}

. Find the tension in each side of the cable.

Traffic light on sagging cable — find cable tension T

Example 11

hard

A child sits on a swing at rest. Her weight is

300 \text{ N}

, the swing chain makes

20°

with vertical because a parent pulls horizontally. What is the horizontal pull?

Child on swing at rest — find horizontal pull force

Example 12

challenge

2 \text{ kg}

block rests on a wedge of

30°

. The wedge sits on a frictionless floor and is given horizontal acceleration

a

such that the block does not slide relative to the wedge (no friction between block and wedge either). Find

a

. Use

g = 9.8 \text{ m/s}^2

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A car travels at a constant velocity of

20 \text{ m/s}

on a straight road. What is the net force acting on the car?

Example 2

medium

A bus travels at

12 \text{ m/s}

and brakes suddenly. A backpack on the floor slides forward. According to Newton's first law, what was the backpack's velocity immediately before friction acted on it?

Example 3

easy

A hockey puck slides on frictionless ice at constant velocity. What is the net force on it?

Example 4

easy

Newton's first law is also called the law of what?

Example 5

easy

A book lies still on a desk. According to the first law, what must be true of the forces?

Book at rest on a desk — forces balanced

Example 6

easy

Why do passengers lurch forward when a car suddenly brakes?

Example 7

easy

Does an object moving at constant velocity require a net force to keep moving?

Example 8

easy

A spacecraft drifts in deep space with its engines off. What happens to its velocity?

Example 9

easy

A car turns at constant speed around a curve. Is there a net force?

Example 10

easy

Tablecloth pulled fast leaves dishes nearly in place. What property explains this?

Example 11

medium

4\text{ kg}

box sits at rest. A

12\text{ N}

push right and a

12\text{ N}

friction left act. Describe its motion.

4 kg box in static equilibrium — horizontal forces cancel

Example 12

medium

1000\text{ kg}

car cruises at constant

20\text{ m/s}

. Engine thrust is

800\text{ N}

forward. What is the resistive (drag+friction) force?

Car at constant velocity — find the resistive force

Example 13

medium

Two equal teams pull a rope, neither side moving. What is the net force on the flag at the center?

Example 14

medium

A ball rolls on a level frictionless surface at

3\text{ m/s}

. Predict its speed after

10\text{ s}

Example 15

medium

In an accelerating bus, a hanging strap tilts backward. Why?

Example 16

medium

2\text{ kg}

object moves at constant velocity. Forces

10\text{ N}

right,

4\text{ N}

left, and

F

left act. Find

F

Object at constant velocity — find unknown force F

Example 17

challenge

5\text{ kg}

crate is shoved and slides to a stop in

4\text{ s}

from

8\text{ m/s}

. Show why the first law is not violated and find the friction force.

Example 18

challenge

3\text{ kg}

lamp hangs by two symmetric cords, each at the same angle, lamp at rest (

g=10

). What is the vertical component sum of the cord tensions?

Lamp hanging from two symmetric cords — vertical tension components sum to 30 N

Example 19

challenge

A coin sits on a card over a cup. The card is flicked sideways and the coin drops into the cup. Explain using the first law and identify why the coin barely moves sideways.

Example 20

medium

4\text{ kg}

sled moves at constant

5\text{ m/s}

while a rope pulls it with

12\text{ N}

. Find the friction force.

Sled at constant velocity — friction force equals rope tension

Example 21

medium

A puck on frictionless ice is given a shove and released. Predict its long-term motion.

Example 22

medium

2\text{ kg}

object hangs at rest from a spring. Spring force is

F

up, weight

19.6\text{ N}

down (

g=9.8

). Find

F

Mass hanging at rest from a spring — find spring force F

Example 23

easy

A truck travels in a straight line at constant velocity

25 \text{ m/s}

. What is the net force on the truck?

Example 24

easy

A spacecraft drifts in deep space, far from any star. No engine fires. What happens to its velocity?

Example 25

medium

0.5 \text{ kg}

puck slides on frictionless ice at constant

4 \text{ m/s}

. A

2 \text{ N}

wind force blows perpendicular to its motion for

1 \text{ s}

. What is the acceleration during this time?

Example 26

medium

An ice skater glides at

3 \text{ m/s}

in a straight line. She experiences a friction force of

0.3 \text{ N}

, and her mass is

50 \text{ kg}

. Is she in equilibrium? What is her acceleration?

Example 27

medium

A cargo box of mass

40 \text{ kg}

slides in a truck at constant velocity

5 \text{ m/s}

. Coefficient of friction between box and truck bed is zero. The truck suddenly brakes to

a_{\text{truck}} = -3 \text{ m/s}^2

. What does the box do?

Example 28

medium

2 \text{ kg}

object moves at

10 \text{ m/s}

east. Three forces act briefly and cancel each other. What is the velocity after they cancel?

Example 29

medium

An object floats at rest in water (buoyancy balances gravity). Why doesn't it sink?

Example 30

hard

Inside a train accelerating to the right at

a

, a pendulum hangs at angle

\theta

from vertical (toward the back). What is

\tan\theta

in terms of

a

and

g

Example 31

hard

A satellite orbits Earth at constant speed in a circular orbit. Is it in equilibrium according to Newton's first law? Explain.

Example 32

hard

Galileo's thought experiment: a ball rolls down one ramp and up another. As friction is reduced, what happens to the height it reaches? What does this imply for a perfectly smooth horizontal surface?

Example 33

hard

A balloon rises at constant velocity. Its weight is

80 \text{ N}

, buoyant force is

B

, and air drag is

30 \text{ N}

downward. Find

B

Balloon at constant ascent velocity — find buoyant force B

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Related Concepts

Force Velocity Inertia Friction

Background Knowledge

These ideas may be useful before you work through the harder examples.

forcevelocity