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Speed, velocity and acceleration

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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?

- Consider direction

1Both Mr Rabbit and Mr Tortoise took the same round trip, but Mr Rabbit slept & returned later.

Who runs faster?

No, I travelled

longer distance every

minute.

Me, as I spent

less time on the

trip.

Comment on their their argument.

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, Instantaneous, Constant

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.

speed at any instant

The word ‘speed’ alone instantaneous speed

Instantaneous speed

distance travelled inan extremely short time interval

Simulation

Speedometer tells the car’s speed at any instant!

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

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

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

rightward but speeding up or accelerating

- Graph distance on the y-axis and time on the x-axis

- Slope = rise = distance = speed
run time

- 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.

- 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

Average, Instantaneous, Constant

direction

magnitude

(speed)

Velocity is...

a speed in a given direction or

rate of change of displacement.

a vector

quantity

velocity

Train drivers concern speed only.

speed = 90 km/h

Pilots concern velocity (direction & speed).

speed = 300 km/h

direction = west

overall displacement

Average velocity =

total time of travel

direction of overall displacement

direction of velocity =

The velocity atany instant is calledinstantaneous velocity.

If a car moves at a constant velocity...

… its average and instantaneousvelocities

have the same value.

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

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

- 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.

- 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.

( )

Average speed =

10.49

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

What is the average speed?

100

= 9.53 m/sor 34.3 km/h

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?

Who runs in a higher average velocity?

AMaria.

BKaren.

CUndetermined since their paths are unknown.

DIncomparable since they run alongdifferent directions.

Average speed of an object magnitude of its average velocity.

(T/F)

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.

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.

(T/F)

direction

speed

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.

- 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

Dv

a

t

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

- An object moving in a circle at constant speed is always accelerating (changing direction).

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

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

rightward but speeding up or accelerating

- 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.

- What is the magnitude of the object’s total displacement after 4 seconds
- What is the average speed after 3 seconds?

8m

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)

+ve

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

Unit of time: hour (h)

Unit of distance/displacement: kilometer (km)

Quantity Unit Scalar/Vector

Speed ______ _____

Velocity ______ _____

Change in velocity ______ _____

Acceleration ______ _____

km h–1

scalar

km h–1

vector

km h–1

vector

km h–2

vector