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Speed, velocity and acceleration. Motion. When an object changes its position, motion has occurred. Distance- How far an object has moved . Displacement- How far an object has moved in relation to its starting point . Consider direction

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  • When an object changes its position, motion has occurred.
    • Distance- How far an object has moved.
    • Displacement- How far an object has moved in relation to its starting point.
        • Consider direction

Example: Two runners travel along the same straight path in a straight line for 500 meters. At the end of the run their distances are the same but their displacements are different. How can this be so?


Who runs faster?

No, I travelled

longer distance every


Me, as I spent

less time on the


Comment on their their argument.

speed distance an object travels per unit of time
SPEED Distance an object travels per unit of time

Relationships between speed, distance, and time:

Speed = Distance/ Time= d/ t

  • Constant Speed- speed does not change over time
  • Average Speed- speed of motion when speed is changing

Avg Speed = Total Distance/ Total Time

  • Instantaneous Speed- speed at any given moment in time (speedometer)

How can we describe how fast an object moves?

A car on Tolo Highway travels 90 km in 1 hour.

We say that the car travels at a speedof 90 km/h.


How can we describe how fast an object moves?

Speed is a measure of how fast something moves.

Speed = distance travelled per unit of time

or km/h(for long distances)

SI unit: m/s

average speed
Average speed

A car travels at 50 km/h

slows down to 0 km/h

and speeds up again to 60 km/h

Its average speed over the whole journey

overall distance travelled


total time of travel


Average speed does not tell the variations during the journey.

On most trips, the speed at any instant is often different from the average speed.

instantaneous speed
Instantaneous speed

speed at any instant

The word ‘speed’ alone  instantaneous speed

Instantaneous speed

 distance travelled inan extremely short time interval


instantaneous speed1
Instantaneous speed

Speedometer tells the car’s speed at any instant!

constant speed
Constant Speed

Not changing speed. Same amount of speed from beginning to last.

motion graphs position vs time
Motion Graphs – Position vs. Time

constant, rightward (+) velocityof +10 m/s

a rightward (+), changing velocity- that is, a car that is moving

rightward but speeding up or accelerating

graphing motion
Graphing Motion
  • Graph distance on the y-axis and time on the x-axis
  • Slope = rise = distance = speed

run time

distance time graph
Distance - Time Graph
  • If something is not moving, a horizontal line is drawn.
  • If something starts out slow and then speeds up, its change in speed can look like this.
learning checkpoint
Learning Checkpoint
  • This graph shows several stages of motion:
    • Stage 1: 100 m in 10 s
    • Stage 2: 50 m in 10 s
    • Stage 3: 150 m in 20 s
  • Calculate the speed as indicated by each of the colors.
  • Calculate the average speed.
  • What is the total distance?
  • What is the displacement?

Stage 1: S= d/ t

100 m/ 10 s= 10 m/s

Stage 2: S= d/t

50 m/ 10 s= 5 m/s

Stage 3: S= d/t

150 m/ 20 s= 7.5 m/s

Ave Speed= Tot d/ Tot t

300 m/ 40 s= 7.5 m/s

Distance = 300 meters

Displacement = 0 meters






Velocity is...

a speed in a given direction or

rate of change of displacement.

a vector



speed with direction
Speed with direction

Train drivers concern speed only.

speed = 90 km/h

Pilots concern velocity (direction & speed).

speed = 300 km/h

direction = west

average velocity
Average velocity

overall displacement

Average velocity =

total time of travel

direction of overall displacement

direction of velocity =

instantaneous velocity
Instantaneous velocity

The velocity atany instant is calledinstantaneous velocity.

If a car moves at a constant velocity...

… its average and instantaneousvelocities

have the same value.

constant velocity

Not changing speed. Same amount of speed from beginning to last.

velocity time graph
Velocity Time Graph

Copy the data chart and construct a VELOCITY vs. TIME Graph

terminal velocity
Terminal Velocity
  • Terminal velocity- the velocity at which the upward force of air resistance equals the downward force of gravity.
  • Once you reach this velocity you will no longer accelerate. (just stay at the same velocity)
  • Parachutes increase your surface area to increase your air resistance in order to reduce your terminal velocity so you don’t die when you hit the ground.
velocity questions
Velocity Questions
  • How far does Bob run if he maintains an average velocity of 3 m/s for 10 s?
  • List three ways you can change the velocity of your car.
  • Is it possible to go around a corner without changing velocity? Explain.
  • One car is going 25 miles/hr north, another car is going 25 miles/hr south. Do they have the same velocity? Explain.
q1 the world record

( )

Average speed =


Q1 The world record...

The world record of women 100-m race is 10.49 s.

What is the average speed?


= 9.53 m/sor 34.3 km/h

q2 in an orienteering event
Q2 In an orienteering event...

In an orienteering event, Maria and Karen reach their control points at the same time.

start, 10:00 am

Maria, 10:30 am

Karen, 10:30 am

Who runs in a higher average velocity?

q2 in an orienteering event1
Q2 In an orienteering event...

Who runs in a higher average velocity?

A Maria.

B Karen.

C Undetermined since their paths are unknown.

D Incomparable since they run alongdifferent directions.

q3 true or false
Q3 True or false:

Average speed of an object  magnitude of its average velocity.


Note: The distance travelled is equal tomagnitude of displacement only if it is a straight-line motion.Speed is usually larger than the magnitude of velocity.

q4 true or false
Q4 True or false:

A man takes a walk starting from rest andending at rest.

It is possible for him to attain an averagespeed of 5 km h–1 but he never goes faster than5 km h–1.





Acceleration measures the change in velocity

Acceleration = velocity per unit time

overall change in velocity


total time taken

vector quantity

Unit: m/s / s

= m/s2


When a car moves faster and faster,

its speed is increasing (velocitychanged).


When a car moves slower and slower,

its speed is decreasing (- velocity changed).


When a car changes direction,

its velocity changes too.

solving acceleration problems using acceleration triangle
Solving Acceleration Problems using Acceleration Triangle
  • If you have starting and ending velocity or speed, find that before you use the triangle.
  • If not, use triangle to find change in velocity (Dv), then find initial or final velocity
  • Dv = ending velocity – starting velocity




3 acceleration
3 Acceleration

If a car accelerates at 2 m/s, what does that mean?

v = 0

t = 0

v = 2 m/s,

v = 2 m/s

t = 1 s

1 m

v = 4 m/s,

v = 2 m/s

t = 2 s

3 m

t = 3 s

v = 6 m/s,

v = 2 m/s

5 m

acceleration at constant speed
Acceleration at constant speed
  • An object moving in a circle at constant speed is always accelerating (changing direction).
motion graphs velocity vs time
Motion Graphs – Velocity vs. Time

constant, rightward (+) velocityof +10 m/s

a rightward (+), changing velocity- that is, a car that is moving

rightward but speeding up or accelerating

acceleration questions
Acceleration Questions
  • A dragster going at 10 m/s increases its velocity to 25 m/s in 4 seconds. What is its acceleration?
  • The driver of a car steps on the brakes, and the velocity drops from 20 m/s to 8 m/s in a time of 2 seconds. Find his acceleration.
  • Find the acceleration of a car that travels at a constant velocity of 40 Km/hr for 10 s.
  • Challenge: Calculate the velocity of a skateboarder who accelerates from rest for 4 seconds down a ramp at an acceleration of 5 m/s2.
graph question
Graph Question
  • What is the magnitude of the object’s total displacement after 4 seconds
  • What is the average speed after 3 seconds?


V= d/t

V= 8m/3s

V= 2.66 m/s

  • Distance and time measurements can be used to describe the velocity and acceleration
  • The Shape of the Distance vs. Time determines the type of motion
    • Rest : Straight line parallel to time axis
    • Constant Speed : Straight line on a slope (magnitude of the speed)
    • Constant Acceleration: Curved line
  • The Shape of the Velocity vs. Time determines the type of motion
    • Rest : Straight line on the time axis
    • Constant Speed : Straight line parallel to the Time axis
    • Constant Acceleration: Straight line on a slope (magnitude of the Acceleration)
q1 a running student


Q1 A running student...

A running student is slowing down in front of a teacher.

With reference to the sign convention,

Velocity of student: positive / negative

Acceleration of student: positive / negative

q2 when time is measured
Q2 When time is measured...

Unit of time: hour (h)

Unit of distance/displacement: kilometer (km)

Quantity Unit Scalar/Vector

Speed ______ _____

Velocity ______ _____

Change in velocity ______ _____

Acceleration ______ _____

km h–1


km h–1


km h–1


km h–2