1) A policeman used a video camera and radar to claim that a car accelerated from 0 to 90 km/h over 150m in 12 seconds. Using the equations of motion, the calculated acceleration of 2.08 m/s^2 supports that this is possible. 2) The document discusses equations of motion, including definitions of acceleration, velocity, distance, and derivations of the three kinematic equations relating these variables. 3) Examples are given for using the kinematic equations to calculate final velocity, distance travelled, or initial/final velocity given two of acceleration, time, or distance.

1. Speeding up, slowing down?

2. Speeding up, slowing
down
Physics on the Road
Lesson 7

4. Constant acceleration
When something gains speed at a constant
rate this is called uniform acceleration.
Lets begin with motion in a straight line
vv∆vv+∆v∆v
∆t∆t∆t t=0
v
v +∆v
v +2∆v

5. Traffic Incident
A policeman using a video camera and radar claims that a car
starting from some lights reached 90 km/h when it passed a
shop 150m away 12 s later. The driver claims this is
impossible.
Distance =150 m
Initial velocity = 0 m/s
Final velocity = 90 km/h
= 25 m/s
Time = 12 s
Check 1: many cars advertise a
0-100 km/h of less than 10s
Check 2: The car would need to gain
25/12=2.08m/s each of the
12 seconds or 2.08 m/s/s
metres per second per second is the unit of acceleration
and is abbreviated to ms-2.

6. Traffic Incident cont…
A policeman using a video camera and radar claims that a car starting from some lights
reached 90 km/h when it passed a shop 150m away 12 s later. The driver claims this is
impossible.
Distance =150 m
Initial velocity = 0 m/s
Final velocity = 25 m/s
Time = 12 s
Car accelerating to 25m/s in 12s
0
5
10
15
20
25
0 1 2 3 4 5 6 7 8 9 10 11 12
Time /s
speed/m/s
∆v
∆t
acceleration = change of velocity
time
acceleration = 25 = 2.08 ms-2
12
avg. speed = change of distance
time
avg. speed = 150 = 12.5 ms-1
12
avg. speed = 0 + 25 = 12.5 ms-1
2
distance = avg. speed x time = 12.5 x 12= 150m

7. Linking to distance time graphs
 Draw this velocity
time graph
 Use your graph and
the relationship
between average
speed and distance
travel to complete a
distance time table.
 Plot the distance
time graph
Car accelerating to 25m/s in 12s
0
5
10
15
20
25
0 1 2 3 4 5 6 7 8 9 10 11 12
Time /s
speed/m/s
distance = avg. speed x time = 12.5 x 12= 150m
Time /s Distance /m
12 150
Distance travelled is the area
under a velocity time graph

8. Kinematic equations
acceleration = change of velocity
time
acceleration = final velocity – initial velocity
time
a = v – u
t
at= v – u
v= u + at
Car accelerating to 25m/s in 12s
0
5
10
15
20
25
0 1 2 3 4 5 6 7 8 9 10 11 12
Time /s
speed/m/s
Distance travelled is the area under the graph
Area of triangle = ½ x base x height
= ½ x time x change in velocity
= ½ x 12 x 25 = 150 m
First equation
What if the object wasn’t originally stationary?

9. More kinematic equations
velocity time graph
0
1
2
3
4
5
6
7
8
0 1 2 3 4
time (s)
velocity(m/s)
The distance
travelled is the
area under the
graph
Area A + Area B
A
B
u
v
u x t + ½ x t x (v-u)
but… at = v – u
so…
s = ut + ½ at2
2nd
equation

10. Third equation of motion
v= u + at
t= v – u
a
average velocity= u + v
2
Distance = average velocity x time
So….
s=u+v t
2
s = (u+v )x (v-u)
2 a
s = v2 – u2
2a
(u+v)(v-u)= v2 – u2
v2 = u2 + 2as3rd equation
1st equation

11. Newton’s equations of motion
v= u + at v2 = u2 + 2ass = ut + ½ at2
Use to compute
final velocity from
acceleration and
time.
Use to compute
distance from
acceleration and
time.
Use to compute
Final velocity
from acceleration
and distance.
v – final velocity (ms-1) t – time (s)
u – initial velocity (ms-1) s –distance/displacement (m)
a – acceleration (ms-2)

12. Questions
v= u + at
v2 = u2 + 2as
s = ut + ½ at2
A car travelling at
10 ms-1
accelerates at
3ms-2 for 5
seconds what is
the car’s final
velocity?.
How far will the
car travel whilst
accelerating?
A coin is dropped
from the Centre Point
tower in Sydney. The
tower is 309m high.
Acceleration due to
gravity is 10 ms-2.
What speed does the
coin hit the ground?
What assumption
have you made?
Q 1 a Q 1 b
Q 2