1. KINEMATICS
A Study of Motion

2. Motion in a Straight Line
A sprinter runs 100m in 10s.
What picture can we get of the sprinters motion?
This statement tells us nothing about the complicated motion of the sprinter's arms and legs. It only describes the motion of the sprinter, as a whole.
A drag car is another example of motion in a straight line.

3. Distance & Displacement
Distance (m)
Is how far a body travels during motion
Scalar Quantity
Displacement (m)
Is the position of an object relative to the origin
Vector Quantity
Pendulum Animation

4. Velocity & Speed Speed (ms-1) Is how fast an object is moving
Scalar Quantity
Velocity (ms-1)
Is how fast an object is moving in a particular direction
Vector Quantity

5. Average Speed & Velocity
Average Speed (ms-1)
Is a measure of how distance travelled changes with time
vave= distance travelled
time taken
Scalar Quantity
Average Velocity (ms-1)
Is a measure of how displacement changes with time
vave= displacement
time taken
Vector Quantity

6. Is a measure of how velocity changes with time
Acceleration
Acceleration (ms-2)
Is a measure of how velocity changes with time
Acceleration = change in velocity or a = v = vf – vi
change In time t t
Since velocity is a vector quantity, acceleration must also be a vector quantity
Note
Since acceleration is a measure of the change in velocity, we have an acceleration if the object changes direction, even if the magnitude of the velocity remains constant.

7. Acceleration Negative Acceleration (ms-2)
A negative acceleration indicates deceleration or the object slowing down.
Example
If an object slows down from 10m/s to 5m/s in 5s, then the
a = v = vf – vi = 5 – 10 = -5 = -1ms-2
t t
Work through question 9 from chp 5.1, pg 162

8. Displaying the action on a Graph
Having made measurements of the motion of an object, it is usually convenient to display the measurements on a graph.
Displacement V Time
Velocity V Time
Acceleration V Time

9. Information from a d-t graph
Constant Velocity
Gradient =rise = Δx = velocity
run Δt
Varying Velocity
In this case the d-t graph is not a straight line everywhere.
To obtain the velocity at anytime during the motion we need to draw the tangent at that point.
INSTANTANEOUS VELOCITY
Constant Velocity Animation

10. Information from a d-t graph
Constant Velocity
Solution
Gradient =rise = Δx = velocity
run Δt
Gradient = 50 = 2m/s 25
The velocity between t=0 and t=25 seconds is +2m/s.
Find the velocity between t=0s and t=25s.
What will be the velocity between t=25s and t=35s?
What will be the velocity between t=35s and t=60s?
0m/s
-1m/s

11. Information from a d-t graph
Varying Velocity
Solution
Gradient =rise = Δx = velocity
run Δt
Gradient = -5 = -0.56m/s 9
The velocity at t=18s is 0.56m/s south.
Find the velocity at t=18s.
What type of velocity is this?
Instantaneous Velocity
Work through questions 1 – 7 from chp 5.2, pg 170

12. Information from a v-t graph
Constant Acceleration
Gradient =rise = Δv = acceleration
run Δt
Constant Acceleration
Area = Displacement
Note: We can have negative displacement, if the velocity is negative (see next slide)
Constant Acceleration Animation

13. Information from a v-t graph

14. Information from a v-t graph
Special Case
A special case is when the velocity is constant.
What would the acceleration be?
The acceleration will be 0m/s2.
What would the v-t graph look like?
Constant Acceleration Animation

15. Information from a v-t graph
Constant Acceleration
Solution
Gradient =rise = Δv = acceleration
run Δt
Gradient = -3 = -1.5m/s2 2
The acceleration between t=4 and t=6 seconds is -1.5m/s2.
Find the acceleration between t=4s and t=6s.
What will be the acceleration between t=0s and t=4s?
What will be the acceleration between t=9s and t=10s?
0m/s2
1m/s2

16. Information from a v-t graph
Constant Acceleration
Solution
Displacement = Area under graph
Area = vt + 0.5vt
= (3×4) + 0.5(3×2)
= =+15m
The displacement between t=0 and t=6 seconds is +15m.
Find the displacement between t=0s and t=6s.
What will be the displacement between t=0s and t=10s?
+13m
Work through questions 9 – 11 from chp 5.2, pg 171

17. Information from a v-t graph
Varying Acceleration
Gradient =rise = Δv = acceleration
run Δt
Constant Acceleration Animation