The First and Second Laws of Motion
TOPIC: Force and Motion
DESCRIPTION: A set of mathematics problems dealing with Newton's Laws of Motion.
CONTRIBUTED BY: Carol Hodanbosi
EDITED BY: Jonathan G. Fairman - August 1996
Newton's First Law of Motion states that a body at rest will
remain at rest unless an outside force acts on it, and a body in
motion at a constant velocity will remain in motion in a straight
line unless acted upon by an outside force.
If a body experiences an acceleration ( or deceleration) or a
change in direction of motion, it must have an outside force acting
on it. Outside forces are sometimes called net forces or unbalanced
The property that a body has that resists motion if at rest, or
resists speeding or slowing up, if in motion, is called
inertia. Inertia is proportional to a body's mass, or the
amount of matter that a body has. The more mass a body has, the more
inertia it has.
The Second Law of Motion states that if an unbalanced force
acts on a body, that body will experience acceleration ( or
deceleration), that is, a change of speed. One can say that a
body at rest is considered to have zero speed, ( a constant speed).
So any force that causes a body to move is an unbalanced force. Also,
any force, such as friction, or gravity, that causes a body to slow
down or speed up, is an unbalanced force. This law can be shown by
the following formula
- F is the unbalanced force
- m is the object's mass
- a is the acceleration that the force causes
If the units of force are in newtons, then the units of mass are
kilograms and the units of acceleration are m/s2. If the
units of force are in pounds (English), then the units of mass are in
slugs, and the units of acceleration are ft/s2.
Motion of an object that is not accelerated (moving at a constant
speed and in a straight line) can be found using the formula
d= v t
- d is the distance traveled
- v is the rate of motion (velocity)
- t is the time
Some sample problems that illustrates the first and second laws of
motion are shown below:
If the speed of sound on a particular day is 343 m/s, and an echo
takes 2.5 seconds to return from a cliff far away, can you determine
how far the cliff is from the person making the sound?
An echo is a sound that travels out and back. It take 2.5 seconds
for this trip, which is twice the distance to the cliff. Therefore,
it only takes 1.25 seconds for the sound to reach the cliff. By
d = v t
d = (343 m/s) (1.25 s)
d = 429 m
F = ma
If an unbalanced force of 600 newtons acts on a body to accelerate it
at +15 m/s2, what is the mass of the body?
m = 600n/15 m/s2
m= 40 kg
- If a car is traveling at 50 km/hr along a straight line, how
many meters does it travel in 10 seconds?
- A force of 5000 newtons is applied to a 1200 kg car at rest.
What is its acceleration?
- A 10 kg body has an acceleration of 2 m/s2. Find
the net force acting on the body.
- An empty truck with a mass of 2500 kg has an engine that will
accelerate at a rate of 1.5 m/s2. What will be the
acceleration when the truck has an additional load of 1500 kg
- A box resting on a table has a mass of 5.0 kg.
- What is its weight?
- What will be its acceleration when an unbalanced horizontal
force of 40 newtons acts on it?
- What is the weight of an object that has a mass of 60
- A net force of 75 pounds acts on a body of 25 slugs. The body
is initially at rest. What is its acceleration during the action
of the force?
- What is the mass of a 185 pound man? If a 100 pound horizontal
net force acts on the man while he is sitting on a wooden floor,
what will his acceleration be?
Aeronautics Classroom Activities
Aerospace Activities Page
Newton's First law - Airplane Application
Newton's Second Law - Airplane Application
Newton's Second Law - Aircraft Motion