Average SpeedThe speed of an object is the distance it travels a certain time.10 ms-1 means 10 m travelled in one second.50 kmh-1 means 50 km travelled in one hour.
Speeds usually vary throughout a journey.
For this reason, we often calculate the average speed of an object.
Measuring Average Speed
d
tstopwatch
Mark out and measure a distance d.Measure the time taken, to travel distance d.
Calculate the average speed using: timedistance speed average
d
v tx
÷
Quantity Unitspeed ( v )
distance ( d )
time ( t )
metre per second ( ms-1 )
metres ( m )
seconds ( s )
Example 1A van has an average speed of 10 ms-1.Calculate the time it takes the van to travel a distance of 125 m.
m 125d
-1ms 10v
???t
vdt
10125
s 12.5t
Results (running)
d = m
t = s
v = ???
tdv
Results (walking)
-1ms v
d = m
t = s
v = ???
tdv
-1ms v
Instantaneous SpeedInstantaneous speed is the speed at a particular instant.This means it is a very short distance travelled.
Electronic Timer
Light GateLength of Card
The card on the trolley cuts the light beam.The timer starts when the beam is broken.The timer stops when the light beam is restored.
The instantaneous speed is calculated by:
taken timecard of length speed ousinstantane
Q1. Why is an electronic timer used rather than a stopwatch?
Q2. How could a more accurate instantaneous speed be recorded?
Human reaction time would give an inaccurate time.
Shorter length of card.
Example 1A trolley with a card attached to it travels down a ramp and passes through a light gate.
6 cm
The light beam is interrupted for 0.24 s.Calculate the instantaneous speed of the trolley as it passes through the light gate.
cm 6 width card
s 0.24 time dinterrupte
??? speed ousinstantane
taken timecard of length speed ousinstantane
0.240.06
m 0.06
-1ms 0.25 speed ousinstantane
x
÷
AccelerationThe acceleration of an object is its change in speed in one second.
v - u
a t
Quantity UnitAcceleration
( a )
Final Speed ( v )
Initial Speed ( u )
Time (t)
Metre per second per second ( ms-2 )
Metre per second (ms-1 )
Metre per second (ms-1 )
Seconds (s)
Example 1A car accelerates from a speed of 5 ms-1 to a speed of 15 ms-1 in a time of 2.5 seconds.What is its acceleration?
-1ms 15v
-1ms 5u
s 2.5t
tu-va
2.55-15
2.510
???a
2ms 4a
An acceleration of 4ms-2 means that the speed increases by 4ms-1 every second.
Car Initial Speed(ms-1)
Final Speed(ms-1)
Time(s)
Acceleration
(ms-2)Lamborghini 0 28 3.3 8.5
Chevrolet 0 28 3.7 7.6
Aston Martin
0 28 4.8 5.8
Mondeo 0 28 9.9 2.83
Answer the following questions showing ALL your working
DecelerationDeceleration is when an object slows down.
The formula is still used but u (initial speed) will be greater than v (final speed).
tuva
Example 1A car decelerates from 12 ms-1 to 2 ms-1 in 5 seconds.Calculate the deceleration.
-1ms 2v
-1ms 12u
s 5t
tu-va
512-2
510-
???a
2ms -2a
Example 2A car travelling at 15 ms-1 comes to rest in a time of 4 seconds.Calculate the car’s deceleration.
-1ms 0v
-1ms 15u
s 4t
tu-va
415-0
415-
???a
2ms -3.75a
Deceleration is always negative.
Acceleration at Credit Level
Will need to rearrange equation to calculate initial speed (u) and final speed (v).
Final Speed (v)
tu-va
uvt a
t a u-v
t a u v *** NEW FORMULA ***Not on data sheet – memorise.
x
÷v - u
a t
Example 1A car accelerates at 2.5 ms-2 for 3 seconds.The initial speed of the car is 4 ms-1.Calculate the final speed of the car.
s 3t
-2ms 2.5a
-1ms 4u
atuv
32.54
7.54???v1ms 11.5v
Initial Speed (u)Use the equation and substitute the numbers and rearrange.
Example 2A car reaches a speed of 20 ms-1 after accelerating at 2 ms-2 for 4 seconds.Calculate the initial speed of the car.
t a u v
-2ms 2a
-1ms 20v
s 4t ???u
atuv
42u20 8u20
208u 8-20u
-1ms 12u
Speed-Time Graphs
t
v
t
v
t
v
acceleration
constant speed
deceleration
Steeper lines mean quicker acceleration / deceleration.
1
time (s)
speed (ms-1)
3 10 14
12
0
The motion of the object is in 3-sections.
Section 1 Object accelerates from rest.Section 2 Object travels at a constant speed of 12ms-1.Section 3 Object decelerates and comes to a halt.
23
Example 1
time (s)
speed (ms-1)
4 11 14
20
0
(a) Describe the 3-parts of the journey.(b) Calculate the initial acceleration.(c) Calculate the final deceleration.
(a) Describe the 3-parts of the journey.Part 1 Object accelerates from rest to 20ms-1.Part 2 Object travels at a constant speed.Part 3 Object decelerates from 20ms-1 to rest.
(b) Calculate the initial acceleration.
-1ms 20v
-1ms 0u
s 4t
tu-va
40-20
420
???a
2ms 5a
(c) Calculate the final deceleration.
-1ms 20u
-1ms 0v
s 3t
tu-va
320-0
320-
???a
2ms6.67 a
Example 2
(a) Describe motion of the object for each section of the graph.(b) Calculate the acceleration for section 1 and 3 of the graph.(c) Calculate the final deceleration of the object.(d) What is the acceleration at section 4 of the graph?
time (s)
speed (ms-1)
2 5 6
4
0 11 14
10
16
12
45
3
Total Distance Travelled
The total distance travelled can be calculated from a speed-time graph.
Total Distance Travelled = Area Under Speed-
Time Graph
time (s)
speed (ms-1)
3 10 14
12
0
12
3
Example 1
Calculate the total distance travelled.
Total Distance = Area Under Graph = Area 1 + Area 2 + Area 3
bh21 area
12321
24 84 18
m 18
The total distance travelled is:
Area 1
bl area
127
m 84
Area 2
bh21 area
12421
m 24
Area 3
m 126
The average speed over the whole journey can now be calculated.
time totaldistance total speed average
14126
-1ms 9
Example 2A driver approaches traffic lights in his car.He sees the lights change and brakes.The speed time graph of the car, from the instant that the lights change is:
time (s)
speed (ms-1)
0.5 3
6
0
(a) Describe the motion of the car in the first 0.5 s.
(b)Calculate the deceleration of the car.
(c) Calculate the distance travelled by the car after the brakes were applied.
(a) Explain the shape of the graph in the first 0.5 s.During the first 0.5 s of the journey, the car is travelling at
a constant speed of 6 ms-1.
(b) Calculate the deceleration of the car.
s 2.5t
-1ms 6u
-1ms 0v???a
tu-va
2.56-0
2.56-
2ms 2.4a
(c) Calculate the distance travelled by the car after the brakes were applied.
Distance Travelled = Area Under Speed-Time Graph
triangle of area travelled distance
hb21
62.521
m 7.5
