Inertia Examples: 38 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Inertia.

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

Concept Recap

The intrinsic tendency of an object to resist any change in its state of motion, whether at rest or moving.

Heavy things are stubborn—hard to start moving, hard to stop.

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: Inertia 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 inertia 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

2 \text{ kg}

book and a

10 \text{ kg}

box are both at rest on a frictionless table. The same force of

5 \text{ N}

is applied to each. Which object is harder to accelerate, and what is each object's acceleration?

Same 5 N force applied to both objects — more mass means more resistance to acceleration

Answer

a_{book} = 2.5 {m/s}^{2}, a_{box} = 0.5 {m/s}^{2}

First step

Inertia is the resistance of an object to changes in its motion, and it is directly related to mass. The

10 \text{ kg}

box has more inertia.

Full solution

2
Acceleration of the book: $a_{book} = \frac{F}{m} = \frac{5}{2} = 2.5 {m/s}^{2}$
3
Acceleration of the box: $a_{box} = \frac{F}{m} = \frac{5}{10} = 0.5 {m/s}^{2}$

Inertia is the tendency of an object to resist changes in its state of motion. More massive objects have greater inertia and require more force to achieve the same acceleration.

Example 2

medium

A passenger in a car is not wearing a seatbelt. The car, traveling at

15 \text{ m/s}

, suddenly stops in

0.3 \text{ s}

. What happens to the passenger (mass

70 \text{ kg}

) and what force would be needed to decelerate them at the same rate?

Example 3

medium

2\text{ kg}

block and a

10\text{ kg}

block both at rest are pushed by the same constant

4\text{ N}

force for

3\text{ s}

. Compare their final speeds.

Example 4

hard

0.5\text{ kg}

ball moves at

3\text{ m/s}

. A constant

0.5\text{ N}

force opposes motion. How long until it stops?

Practice Problems

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

Example 1

medium

A hockey puck (

0.17 \text{ kg}

) slides on frictionless ice at

25 \text{ m/s}

. A bowling ball (

6 \text{ kg}

) rolls at

3 \text{ m/s}

. Which object has more inertia, and which is harder to stop?

Example 2

hard

An empty shopping cart (

15 \text{ kg}

) and a full one (

60 \text{ kg}

) are both pushed from rest with

40 \text{ N}

for

2 \text{ s}

. What is the final speed of each? How does this illustrate inertia?

Equal 40 N force, but 4× the mass — greater inertia yields only 1/4 the acceleration and 1/4 the speed

Example 3

easy

What property of an object measures its inertia?

Example 4

easy

Which is harder to stop: a

2\text{ kg}

cart or a

10\text{ kg}

cart at the same speed?

Example 5

easy

Is inertia a force?

Example 6

easy

Do moving objects have inertia?

Example 7

easy

A passenger jerks backward when a car accelerates forward. What explains this?

Example 8

easy

Between mass and momentum, which equals inertia?

Example 9

easy

Why does a heavy truck need a longer distance to stop than a light car at the same speed?

Example 10

easy

If two objects feel the same net force, which gains speed faster: the one with more or less inertia?

Example 11

medium

4\text{ kg}

object and an

8\text{ kg}

object feel a

24\text{ N}

force each. Compare accelerations to show the inertia effect.

Example 12

medium

A coin rests on a flicked card and stays nearly put. Which object's inertia matters, and why does the coin not move much?

Example 13

medium

Why are seatbelts important during a sudden stop?

Example 14

medium

On a frictionless surface, a

5\text{ kg}

box moves at

4\text{ m/s}

. What force is needed to keep it moving at that speed?

Zero net force → constant velocity at 4 m/s; inertia sustains motion without any applied force

Example 15

medium

Why is it easier to shake ketchup out by suddenly stopping the bottle's downward motion?

Example 16

medium

Two pucks on frictionless ice: a

1\text{ kg}

and a

3\text{ kg}

. The same

6\text{ N}

force acts on each. After

2\text{ s}

from rest, find each speed.

Example 17

challenge

A magician pulls a tablecloth fast; dishes barely move. If the cloth-dish friction is

2\text{ N}

on a

0.5\text{ kg}

dish for

0.1\text{ s}

, find the dish's speed change.

Brief 2 N friction over 0.1 s changes the dish's speed by only 0.4 m/s — inertia keeps it nearly in place

Example 18

challenge

1200\text{ kg}

car and a

2400\text{ kg}

truck both brake with a

6000\text{ N}

force from

20\text{ m/s}

. Compare their stopping times.

6000 N on 1200 kg car → stops in 4 s; same force on 2400 kg truck → stops in 8 s — double the inertia, double the stopping time

Example 19

challenge

Explain why an astronaut in orbit still finds a massive object hard to push, despite being weightless.

Example 20

medium

6\text{ kg}

and a

2\text{ kg}

cart at

5\text{ m/s}

are stopped by the same

10\text{ N}

force. Compare their stopping times.

Example 21

medium

Why does a passenger sway sideways when a car turns sharply?

Example 22

medium

10\text{ kg}

object on frictionless ice moves at

3\text{ m/s}

. What force keeps it at

3\text{ m/s}

Example 23

easy

5\text{ kg}

object and a

20\text{ kg}

object both feel a

40\text{ N}

force. Find their accelerations.

Example 24

medium

A book sits on a tablecloth. Why is it easier to pull the cloth out quickly than slowly?

Example 25

medium

Which has more inertia: a

3\text{ kg}

ball moving at

20\text{ m/s}

or a

5\text{ kg}

ball at rest?

Example 26

medium

2400\text{ kg}

truck and a

1200\text{ kg}

car both brake at the same deceleration. Compare the braking forces required.

Example 27

medium

10\text{ kg}

object on frictionless ice is given a quick push and slides at

4\text{ m/s}

for

30\text{ s}

. What force acts on it during the slide (after the push)?

Example 28

medium

0.2\text{ kg}

ball on frictionless ice is pushed by

1\text{ N}

for

0.5\text{ s}

, then the force ends. Find its speed at

t = 5\text{ s}

Example 29

hard

1500\text{ kg}

car going

20\text{ m/s}

collides and stops in

0.1\text{ s}

. Compare the average force vs. stopping in

1\text{ s}

(e.g., with crumple zones).

Example 30

hard

Two boxes (

3\text{ kg}

and

9\text{ kg}

) are on frictionless ice. A

36\text{ N}

force is applied to each. How far does each travel in

4\text{ s}

starting from rest?

Example 31

hard

An astronaut (

80\text{ kg}

) in deep space pushes a

200\text{ kg}

satellite with

10\text{ N}

for

5\text{ s}

. Find each object's speed afterward.

Example 32

challenge

Why is rotational inertia (moment of inertia) different from translational inertia, and what does it depend on besides mass?

Example 33

medium

4\text{ kg}

object on frictionless ice moves at

5\text{ m/s}

. To bring it to rest in

2\text{ s}

, what force must be applied?

Example 34

medium

On a frictionless turntable, a small object rests near the center and is then placed near the edge. Which location takes more centripetal force to keep the object moving in a circle when the turntable spins?

← Back to Inertia Practice Mode

Related Concepts

Mass Newton's First Law Momentum

Background Knowledge

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

mass