Force and
Motion
PREPARED BY: TYPE YOUR NAME HERE
S7FE - IIIa - 1
 Describe
the motion of an
object in terms of distance
or displacement, speed or
velocity, and acceleration
Force and Motion
Standards

Students will investigate the relationship
between force, mass, and the motion of objects.

a. Determine the relationship between velocity
and acceleration.

b. Demonstrate the effect of balanced and
unbalanced forces on an object in terms of
gravity, inertia, and friction.
Essential Question:
 What
is the relationship
between velocity and
acceleration?
Supporting Questions:
 How can motion of an
object be determined by a
graph?
Speed, Velocity, and
Acceleration
Goals:
 To
investigate what is needed to
describe motion completely.
 To
compare and contrast speed and
velocity.
 To
learn about acceleration.
An object is in motion if it changes position
relative to a reference point.

Objects that we call stationary—
such as a tree, a sign, or a
building—make good reference
points.
The passenger can use a tree as a reference point to decide if the
train is moving. A tree makes a good reference point because it is
stationary from the passenger’s point of view.
Describing Motion
Whether or not
an object is in
motion depends
on the reference
point you choose.
DISTANCE VERSUS
DISPLACEMENT
The word “quantity” is used to
describe a large amount or number
of something while the word “unit”
is also used to describe a number of
things.
“Quantity” is used when referring to
an indefinite number while “unit” is
used when referring to a definite
number of things.
QUANTITY
UNIT
DISTANCE
Distance
is a scalar
quantity that refers to "how
much ground an object has
covered" during its motion.
Distance
here will be = 4m
+ 3m + 5m = 12 m

Distance here will be = 4m + 3m + 5m = 12 m
Distance
 is
the total movement of
an object without any
regard to direction. We can
define distance as to how
much ground an object has
covered despite its starting
or ending point.
Distance
is the actual path
length travelled by an
object in the given
interval of time during
the motion. It is a
positive scalar
quantity.

Displacement
 Displacement
is defined as the change in
position of an object. It is a vector
quantity and has a direction and
magnitude. It is represented as an arrow
that points from the starting position to
the final position. For example- If an
object moves from A position to B, then
the object’s position changes. This
change in position of an object is known
as Displacement.
Displacement

is the difference between the final
and initial positions of the object in
a given interval of time. It can also
be defined as the shortest distance
between these two positions of the
object and its direction is from the
initial to final position of the
object, during the given interval of
time. It is a vector quantity.
Pytagorean Theorem
PYTAGOREAN THEOREM
Assume your school is located 2 km away from
your home. In the morning you are going to
school and in the evening you come back
home. In this entire trip what is the distance
travelled and the displacement covered?
DISTANCE= 4km
DISPLACEMENT= 0
John walks from the point A to B to C.
What does the distance he travel?
What is the displacement?

DISTANCE= 7m

DISPLACEMENT= 5m
DISTANCE AND DISPLACEMENT
Distance
When an object moves, it goes from point A to point B –
that is the DISTANCE it traveled. (SI unit is the
meter)
Distance is how much ground an object has covered during
its motion.
B
A
Distance

Distance (d) – how far an object travels.

Does not depend on direction.

Imagine an ant crawling along a ruler.

What distance did the ant travel?
0
cm

1d = 3 cm2
3
4
5
6
7
8
9
10
Distance

Distance does not depend on direction.

Here’s our intrepid ant explorer again.

Now what distance did the ant travel?
1
2
3
4
5
0
cm


d = 3 cm
Does his direction change the answer?
6
7
8
9
10
Distance

Distance does not depend on direction.

Let’s follow the ant again.
0
cm
1
2
3
4
5
6
7
8
9

What distance did the ant walk this time?

d = 7 cm
10
Displacement

Displacement (d) – difference between an
object’s final position and its starting position.
 Does
depend on direction.

Displacement = final position – initial position

d = dfinal – dinitial

In order to define displacement, we need
directions.
Examples of directions:
+
and –
N, S, E, W
Angles
Displacement vs. Distance
 Example
The
ant walked 3 cm.
 Example
The
 An
of distance:
of displacement:
ant walked 3 cm EAST.
object’s distance traveled and its
displacement aren’t always the same!
Displacement

Let’s revisit our ant, and this time we’ll find his displacement.
- +

Distance: 3 cm
0 Displacement:
1
2 +3 cm
3
4
5
cm  The positive gives the ant a direction!
6
7
8
9
10
Displacement

Find the ant’s displacement again.

Remember, displacement has direction!
- +
0 Distance:
1
3
32cm
cm
 Displacement: -3 cm
4
5
6
7
8
9
10
Displacement

Find the distance and displacement of the ant.
- +

Distance: 7 cm

Displacement: +3 cm
1
2
3
0
cm
4
5
6
7
8
9
10
Displacement vs. Distance

An athlete runs around a track that is 100 meters
long three times, then stops.
 What
is the athlete’s distance and displacement?

Distance = 300 m

Displacement = 0 m

Why?
DISPLACEMENT
DISTANCE
IS VECTOR
IS A SCALAR
Speed
 Speed
(s) – Rate at which an
object is moving.
 speed = distance / time
 s = d/t
 Like distance, speed does
not depend on direction.
Speed

A car drives 100 meters in 5 seconds.
1s
2
3
4
5
100 m

What is the car’s average speed?

s = d/t

s = (100 m) / (5 s) = 20 m/s
SPEEDOMETER
Speed

A rocket is traveling at 10 m/s. How long does
it take the rocket to travel 30 m?
Speed
A
racecar is
traveling at 85.0
m/s. How far does
the car travel in
30.0 s?
Velocity
 Velocity
(v) – speed with
direction.
 velocity
v
= displacement / time
= d / t
 Has
magnitude and direction!
Magnitude
– a measure that
has a value
What
is the velocity
of a rocket that
travels 8000m in 13s
travelling to the
south?
QUIZ TIME
1.
A car travels at
uniform velocity a
distance of 100 m in 4
seconds. What is the
speed of the car?
2.
If a sprinter runs
100 m in 10 seconds,
what is his average
velocity?
3.
What is the
velocity of a rocket
that
travels 8000m in 13s
travelling to the
south?
4
. How long will
it take if you
travel with an
average speed
of 100m/s?
5.
A boy walks at a
speed of 4 kmph.
How much time does
he take to walk a
distance of 20 km?
6.
A cyclist covers
a distance of 15
miles in 2 hours.
Calculate his
speed.
7.
Victor covers 210
km by car at a speed
of 70 km/hr. find the
time taken to cover
this distance.
8.
A plane’s average
speed between two
cities is 600km/hr. If
the trip takes 2.5hr/
how far does the plane
fly?
Speed
Calculating Speed: If you know the distance an
object travels in a certain amount of time, you
can calculate the speed of the object.
What is
instantaneous
speed?
Instantaneous
speed is the
velocity of an
object at a
certain time.
Speed = Distance/time
Average speed = Total distance/Total time
Velocity
Because velocity depends on direction as well
as speed, the velocity of an object can change
even if the speed of the object remains
constant.
The speed of this car
might be constant,
but its velocity is not
constant because the
direction of motion
is always changing.
Velocity
Velocity is a description of an
object’s speed and direction.
As the sailboat’s direction
changes, its velocity also
changes, even if its speed stays
the same. If the sailboat slows
down at the same time that it
changes direction, how will its
velocity be changed?
Speed v. Velocity
How are speed and velocity similar?
They both measure how fast something is moving
1.
2. How are speed and velocity different?
Velocity includes the direction of motion and
speed does not (the car is moving 5mph East)
Is velocity more like distance or
displacement? Why?
Displacement, because it includes direction.
3.
Graphing Speed
D
I
S
T
Speed
increasing
Object begins moving at
a different speed
A
N
Object is
stopped
C
E
TIME
The steepness of a line on a graph is called slope.

The steeper the slope is, the
greater the speed.

A constant slope represents
motion at constant speed.
Using the points shown, the rise is
400 meters and the run is 2 minutes.
To find the slope, you divide
400 meters by 2 minutes. The slope is
200 meters per minute.
Formula for Calculating Speed
Speed = Distance time
Problem Solving: Calculating Speed
What is the speed of a sailboat that is traveling 120 meters in 60 seconds?
Step 1: Decide what the problem is asking? A boat traveled 120 meters in 60
seconds. What was the speed of the boat?
Step 2: What is the formula to calculate speed? Speed = Distance/Time
Step 3: Solve the problem using the formula:
Speed = 120 meters
60 seconds = 2 m/s
So, the boat was traveling at 2 m/s
Now you try:
What is the speed of a car that is traveling 150
miles in 3 hours?
Answer:
Step 1: What are the facts in the problem?
A car is traveling 150 miles in 3 hours.
Step 2: What is the formula to solve the
problem? Speed = Distance/Time
Step 3: Solve the problem.
Speed = 150 miles
3 hours
Speed = 50 miles/hr.
So, the car is traveling 50 miles/hr.
Acceleration
Acceleration is the rate at which velocity
changes.
Acceleration can result from a change in
speed (increase or decrease), a change
in direction (back, forth, up, down left,
right), or changes in both.

The pitcher throws. The ball speeds toward the
batter. Off the bat it goes. It’s going, going, gone! A
home run!

Before landing, the ball went through several changes
in motion. It sped up in the pitcher’s hand, and lost
speed as it traveled toward the batter. The ball
stopped when it hit the bat, changed direction, sped
up again, and eventually slowed down. Most examples
of motion involve similar changes. In fact, rarely does
any object’s motion stay the same for very long.
Understanding Acceleration
1. As the ball falls from the girl’s hand,
how does its speed change?
2. What happens to the speed of
the ball as it rises from the ground
back to her hand?
3. At what point does the ball
have zero velocity? When it
stops and has no direction.
4. How does the velocity
of the ball change when
it bounces on the floor?
You can feel acceleration!
If you’re moving at 500mph
east without turbulence,
there is no acceleration.
But if the plane hits an air pocket and drops 500 feet in
2 seconds, there is a large change in acceleration and
you will feel that!
It does not matter whether you speed up or
slow down; it is still considered a change in
acceleration.
In science, acceleration refers to increasing speed,
decreasing speed, or changing direction.

A car that begins to move from a stopped position or speeds up to
pass another car is accelerating.

A car decelerates when it stops at a red light. A water skier
decelerates when the boat stops pulling.

A softball accelerates when it changes direction as it is hit.
Calculating Acceleration
Acceleration = Change in velocity
Total time
So…Acceleration = (Final speed – Initial speed)
Time
Calculating Acceleration
As a roller-coaster car starts down a slope, its
speed is 4 m/s. But 3 seconds later, at the
bottom, its speed is 22 m/s. What is its
average acceleration?
What information have you
been given?
Initial speed = 4 m/s
Final Speed = 22 m/s
Time = 3 s
Calculating Acceleration
What quantity are you trying to calculate?
The average acceleration of the roller-coaster car.
What formula contains the given quantities and the
unknown quantity?
Acceleration = (Final speed – Initial speed)/Time
Perform the calculation.
Acceleration = (22 m/s – 4 m/s)/3 s = 18 m/s/3 s
Acceleration = 6 m/s2
The roller-coaster car’s average acceleration is 6 m/s2.
Graphing acceleration
S
P
E
Object
accelerates
Object decelerates
E
D
Object moves
at constant
speed
Time
Now You Try:
A roller coasters velocity at the top of
the hill is 10 m/s. Two seconds later it
reaches the bottom of the hill with a
velocity of 26 m/s. What is the
acceleration of the coaster?
Since the slope is increasing, you can conclude that the speed is
also increasing. You are accelerating.
Distance-VersusTime Graph The
curved line on this
distance-versus-time
graph tells you that
the cyclist is
accelerating.
Acceleration Problems
A roller coaster is moving at 25 m/s at the bottom of a hill. Three seconds later it
reaches the top of the hill moving at 10 m/s. What was the acceleration of the
coaster?
Initial Speed = 25 m/s
Final Speed = 10 m/s
Time = 3 seconds
Remember (final speed – initial speed) ÷ time is acceleration.
(10 m/s – 25 m/s) ÷ 3 s = -15 m/s ÷ 3 s = -5 m/s2
This roller coaster is decelerating.
A car’s velocity changes from 0 m/s to 30 m/s in
10 seconds. Calculate acceleration.
Final speed = 30 m/s
Initial speed = 0 m/s
Time = 10 s
Remember (final speed – initial
speed) ÷ time is acceleration.
(30 m/s – 0 m/s) ÷ 10 s = 30 m/s ÷ 10 s = 3 m/s2
A satellite’s original velocity is 10,000 m/s.
After 60 seconds it s going 5,000 m/s. What
is the acceleration?
Remember (final speed – initial speed) ÷ time is acceleration.
Final speed (velocity) = 5000 m/s
Initial speed (velocity) = 10,000 m/s
Time = 60 seconds
(5000 m/s – 10,000 m/s) ÷ 60 s = -5000 m/s ÷ 60 s
= -83.33 m/s2
**This satellite is decelerating.

If a speeding train hits the brakes and it takes
the train 39 seconds to go from 54.8 m/s to 12
m/s what is the acceleration?
Remember (final speed – initial speed) ÷
time is acceleration.
Final speed= 12 m/s
Initial speed= 54.8 m/s
Time = 39 s
12 m/s – 54.8 m/s ÷ 39 s = -42.8 m/s ÷ 39 s
= -1.097 m/s2
This train is decelerating.
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