1.2 form 3 speed, velocity and acceleration
TRANSCRIPT
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Speed, velocity and acceleration
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1. Scalar quantity
2. Vector quantity
3. Distance
4. Displacement
5. Speed
6. Velocity
7. Acceleration
8. Deceleration
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Definitions
1. Scalar quantity: a quantity that has only magnitude. E.g. mass, temperature, distance e.t.c.
2. Vector quantity: a quantity that has both magnitude and direction e.g. weight, displacement, force, acceleration e.t.c.
3. Distance: this is the amount of space between two points. It is a scalar quantity and measured in meters, centimeters, kilometers, miles, light years e.t.c. The SI unit is meter (m).
4. Displacement: This is distance in a particular direction. E.g. 5km North, 15centimeters West
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5. (a) Speed: this is distance covered per unit time.
It is a scalar quantity and is measured in meters per
second (m/s), kilometers per hour (km/h), e.t.c. The
SI unit for speed is meter per second (m/s).
speed= distance (m)
time (sec)
(b) Average speed: this is given by:
average speed = total distance (m)
total time taken (s)
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6. Velocity: … is displacement per unit time. It is
also defined as distance covered in a particular
direction per unit time OR speed in a particular
direction. It is a vector quantity and is measured in
meters per second (m/s).
For motion in a straight line, + or – is used to indicate
direction:
+10 m/s
- 10 m/s
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7. Acceleration: this is change of velocity per
unit time. It can also be defined as the rate change
of velocity. It is a vector quantity. The SI unit is
meters per second squared (m/s2) or (ms-2)
8. Deceleration: this is a negative acceleration.
It is also called retardation.
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Equations of motion
1. v = u + at
2. x = ut + 1/2 at2
3. V2 = u2 + 2ax
4. Vavg = V + u2
5. Sp. = D/t
Where;
v = final velocity
u = initial velocity
vavg = average velocity
a = acceleration
t = time
x = displacement
Sp. = Speed
D = Distance
t = time
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Examples
1. A car travels 600m in 30s. What is its average
speed?
2. A car has a steady speed of 8m/s.
a) How far does the car travel in 8s?
b) How long does the car take to travel 160m?
3. A car takes 8s to increase its velocity from 10m/s to
30m/s.
a) What is its acceleration?
b) Calculate the distance covered.
c) Determine its average velocity.
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Revision exercise 1.1
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MOTION GRAPHS
1. Distance – time
graphs
- The distance
covered by a car can
be measured every
second. This can be
represented on a
graph.
- On a graph, the y-
axis is the distance
and the x-axis is the
time taken.
- The gradient is equal
to the speed.
Time (s)
Distance
(m)
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Exercise
The distance traveled by truck was measured at intervals. The information was recorded in the table below. Use the information to draw a distance – time graph.
Determine the speed of the truck
a) between 1s and 3sec.
b) between 4s and 6s
Time/s 0 1 2 3 4 5 6
Distance/m 0 10 20 30 40 40 40
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2. Velocity – time graphs
- For the speed time graph, velocity is on the y-
axis and time on the x-axis.
- The gradient of the graph is equal to the
acceleration.
Time (s)
Velocity
(m/s)
The area under the graph is equal to the distance covered.
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example
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Exercise
Consider the velocity – time graph below.
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9
velo
cit
y (
m/s
)
time (s)
1. Calculate the acceleration during the first 2 seconds.
2. What is the acceleration between the 2nd and 4th seconds of the motion?
3. Determine the deceleration.
4. Calculate;
a. Distance covered in the first 2 seconds
b. Total distance covered
5. Total distance covered