Speed, velocity and acceleration

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

Who is right?

Me, as I spent less time on the

trip.

No, I travelled more distance every

second I ran.

Who runs faster?

2 Some kid is lost in the woods.

(a) If he walks at a speed of 4 km/hr, try to locate his possible positions on the map.

2 Some kid is lost in the woods.

(b) What else is important to find the kid?The direction in which he has been

walking.

Reference Points

All Motion is relative

• All motion is relative to a reference.

• This means that we describe motion of an object relative to some other object

All Motion is relative

• In our environment, the reference for motion is the earth’s surface, and speeds are measured relative to the earth

• The earth moves at 107,000 km/h relative to the sun

Calculating Motion and Speed

1 Speed

How can we describe how fast an object moves?

E.g. A car on Beltway 8 travels 90 km in 1 hour.

We say that the car travels at a speed of 90 km/hr.

1 Speed

Speed is a measure of how fast something moves.

Speed = distance travelled per unit of time

Speed = distance travelled per unit of timeSI unit: m/s or km/h (for long distances)

How can we describe how fast an object moves?

and speeds up again to 60 km/.and speeds up again to 60 km/.

a Average speed

Its average speed over the whole journeyoverall distance travelled

total time of travel

slows down to 0 km/h, slows down to 0 km/h,

A car travels at 50 km/h,A car travels at 50 km/h,

1 Speed

=

Question 1

• A bug crawls 10 cm in 5 sec. What was the bug’s approximate speed in cm/sec?

2 cm/sec

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.

a Average speed1 Speed

b Instantaneous speed

= speed at any instantInstantaneous speed

1 Speed

The word ‘speed’ alone instantaneous speedInstantaneous speed

distance travelled in an extremely short time interval

Speedometer tells the car’s speed at any instant!

1 Speed

b Instantaneous speed

Question 2

( )Average speed = 10.49 s

= 9.53 m/s

100 m

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

What is the average speed?

Velocity

2 Velocity

rate of change of displacement.

a speed in a given direction or

velocitya

vector quantit

y

direction

magnitude(speed)

Velocity is...

speed = 300 km/hdirection = west

Train engineers use speed only.

a Speed with direction

2 Velocity

Pilots use velocity (direction & speed).

speed = 90 km/h

b Average velocity

Average velocity =overall displacement

total time of travel

direction of velocity = direction of overall displacement

2 Velocity

Question 3

• A student runs around a circular track that is 1000m in length in a time of 30 min. What is the average velocity of the student?

0 m/minIf the student runs completely around the track, they are back

where they began. So their overall displacement is zero.

c Instantaneous velocity

The velocity at any instant is called instantaneous velocity.

If a car moves at a constant velocity...

… its average and instantaneous velocities have the same value.

2 Velocity

Question 4

• Which of these is a correct velocity?A. 55 miles per hour

B. 15 kilometers per second

C. 30 meters per second east

D. 400,000,000 meters per hour

Acceleration

3 Acceleration

When an object moves faster and faster,

its speed is increasing (velocity changed).

3 Acceleration

When an object moves slower and slower,

its speed is decreasing (velocity changed).

When an object changes direction,

3 Acceleration

its velocity changes too.

3 AccelerationAcceleration measures the change in velocity

Acceleration = velocity per unit time

Acceleration = velocity per unit time

direction

speed

overall change in velocitytotal time taken

= m/s2Unit: m/s/s vector quantity

=

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

3 Acceleration

t = 1 sv = 2 m s–1,v = 2 m s–

1

v = 0

t = 2 sv = 4 m s–1, v = 2 m s–

1

v = 6 m s–1, v = 2 m s–1

t = 3 s

1 m

t = 0

3 m

5 m

Tommy accelerates from 20 m/s at 15 sec (t1) to 40 m/s at 60 sec (t2).

Question 5

What is his avg. acceleration between t1 and t2?

Avg. acceleration

=40 m/s – 20 m/s

60s – 15 s20 m/s

45 s=

= .44 m/s2