Form 4 – Unit 2 – Theme 1 – On the Move 1 Theme 1: On the Move This is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Scalars and Vectors Scalars are quantities, which have magnitude alone. Vectors are quantities, which have both a magnitude and a direction. Distance and Displacement Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position. Speed and Velocity Speed is a scalar quantity which refers to "how fast an object is moving." Velocity is a vector quantity which refers to "the rate at which an object changes its position."example - one must describe an object's velocity as being 20 m/s, east. Average Speed and Average Velocity As an object moves, it often undergoes changes in speed. The average speed during the course of a motion is often calculated using the following equation: Average speed = total distance / total time Units - (m/s)
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Theme 1: On the Move · Scalars and Vectors Scalars are quantities, which have magnitude alone. Vectors are quantities, which have both a magnitude and a direction. Distance and Displacement
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Form 4 – Unit 2 – Theme 1 – On the Move 1
Theme 1: On the Move
This is the science of describing the motion of objects using words,
diagrams, numbers, graphs, and equations.
Scalars and Vectors
Scalars are quantities, which have magnitude alone.
Vectors are quantities, which have both a magnitude and a
direction.
Distance and Displacement
Distance is a scalar quantity which refers to "how much
ground an object has covered" during its motion. Displacement is a vector quantity which refers to "how far
out of place an object is"; it is the object's change in position.
Speed and Velocity
Speed is a scalar quantity which refers to "how fast an object is
moving."
Velocity is a vector quantity which refers to "the rate at which an
object changes its position."example - one must describe an object's
velocity as being 20 m/s, east.
Average Speed and Average Velocity
As an object moves, it often undergoes changes in speed.
The average speed during the course of a motion is often calculated
Speeding up means that the velocity is increasing. This is
Acceleration .For instance, an object with a velocity changing from +3 m/s to + 9 m/s is speeding up. An object with a velocity changing from 9 m/s to 0 m/s is speeding down. This is Deceleration.
The gradient for a v-t Graph
If the acceleration is zero, then the gradient is zero (i.e., a horizontal line). (constant velocity or stationary)
If the acceleration is positive, then the gradient is an upward straight line. (Acceleration)
If the acceleration is negative, then the gradient is negative (i.e.,
a downward straight line). (Deceleration)
Determining the Area on a v-t Graph
A velocity vs. time graph can also be used to determine the distance
traveled by an object. For velocity vs. time graphs, the area bounded by the line and the axes represents the distance
traveled.
The shaded area is representative of
the distance traveled by the object during the time interval from 0 seconds to 6 seconds. This takes on the shape
of a rectangle whose area can be
calculated using Length X Breadth.
Form 4 – Unit 2 – Theme 1 – On the Move 6
The shaded area is representative of the distance traveled by the
object during the time interval from 0 seconds to 4 seconds. This takes on the shape of a triangle whose
area can be calculated using ½
Length X Breadth.
The area under graph takes on the shape of a trapezium
whose area can be calculated using the appropriate
equation.
Alternative Method for Calculating the Area of a Trapezium
An alternative method of determining the area of a trapezoid involves breaking the trapezium into a triangle and a rectangle. The areas of the triangle and rectangle are computed individually; the area of the
trapezoid is then the sum of the areas of the triangle and the rectangle.
Form 4 – Unit 2 – Theme 1 – On the Move 7
Graphical Interpretation of Acceleration
Consider a train accelerating from a station along a straight and level track to a maximum speed of 25 m/s in 45 s . It then moves at a constant speed for a further 45 s . It then slowed down to a stop at
the next station in 20 s.
Acceleration is the gradient of the speed-time graph.
From the graph,
between O and A, the train is accelerating; between A and B, the train travels at a constant speed; between B and C, the train slows down. This can be called
negative acceleration, or deceleration. It is given a minus
sign.
Distance is the area under the speed-time graph. To work out the total
distance, we would add the areas of:
triangle OAX; rectangle ABXY;
triangle BCY.
Form 4 – Unit 2 – Theme 1 – On the Move 8
Describing Motion with Equations
1. Distance is how far you travel between any two points by any route. It is a scalar quantity.
2. Displacement is the minimum “as the crow flies” distance between two points. It is a vector quantity, so it has direction.
3. Speed is how fast you go, the rate of change of distance. 4. Velocity is rate of change of displacement. It must have a
direction.
5. Acceleration can be used as both a vector and a scalar
quantity. It is the rate of change of speed or velocity.
Quantity Physics Code Units
Distance s m
Speed at the start u m/s
Speed at the end v m/s
Acceleration a m/s2
Time t s
Speed is simply how fast something is going. we measure it in
metres per second (written as m/s )
speed (m/s) = distance (m) S = s/t time(s)
Acceleration is the change in velocity per unit time . It is measured by the use of the equation:
Where a = acceleration (m/s/s)
v = final velocity (m/s) u = initial (starting) velocity (m/s) t = time (seconds)
v - u is the change in velocity
Form 4 – Unit 2 – Theme 1 – On the Move 9
Using the Equations of Motion
These equations are a set of four equations which can be utilized to determine unknown information about an object's motion if other
details are known.
1.
Arranging acceleration = change in velocity/ time
2.
Distance = average speed × time
4.
Form 4 – Unit 2 – Theme 1 – On the Move 10
When applying these four equations to the motion of an object in free
fall free take note that:
An object in free fall experiences an acceleration of +10
m/s2. If an object is dropped from an elevated height to the ground
below, the initial velocity of the object is 0 m/s.
If an object is projected upwards in a vertical direction, it will slow down as it rises upward. The instant at which it reaches the
peak of its trajectory, its velocity is 0 m/s.
Free Fall and the Acceleration of Gravity
Introduction to Free Fall
A free-falling object is an object which is falling under the sole influence
of gravity.
All free-falling objects (on Earth) accelerate downwards at a rate of
approximately 10 m/s2
The Acceleration of Gravity
A free-falling object has an acceleration on Earth of 10 m/s2,
downward. It is known as the acceleration of gravity . This quantity is such an important quantity that physicists have a special symbol to
denote it – the symbol g.
The distance which a free-falling object has fallen from a position of
rest is also dependent upon the time of fall. The distance fallen after a time of t seconds is given by the formula below:
S = ½ g t2
Since initial velocity is zero.
Form 4 – Unit 2 – Theme 1 – On the Move 11
Thinking, Braking & Total stopping distance.
Road users are advised to maintain safe distances to cut down
the risk of accidents. The shortest stopping distance of a
vehicle depends on its speed and on the road conditions.
Stopping is made up of two parts: thinking and braking.
Thinking time is the reaction time, when your brain is
responding to the hazard ahead of you. Thinking distance
is the distance travelled by the car in the time it takes the
driver to react.
Factors affecting thinking time.
1. Tiredness: Your brain thinks slower - you will not
be able to apply the brakes as quickly.
2. Alcohol : Being under the influence - even legally
- seriously alters how well you can judge hazards.
Your body also moves less accurately. Late or missed
braking results! 3. Drugs : Most drugs make you less alert and less
aware of hazards. Even legal pain-killers and hay-
fever tablets can seriously affect reaction times.
4. Distractions : In-car distractions (e.g. very loud
music, mobile phones, crying babies, etc.) take your
mind off the road ahead.
Braking time is the time taken to slow the vehicle down from
your initial speed to zero . The Braking distance is the
distance traveled by the car from the point where the brakes