Form 4 – Unit 2 – Theme 1 – On the Move 1

Theme 1: On the Move

Kinematics is the science of describing the motion of objects using

words, diagrams, numbers, graphs, and equations.

Vectors, Scalars, Distance, Displacement, Speed, Velocity,

Acceleration

Scalars and Vectors

Scalars are quantities which are fully described by a magnitude

alone.

Vectors are quantities which are fully described by 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.

Describing Motion with Words

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." When evaluating the velocity of an object,

you must keep track of its direction. For instance, you must describe an object's velocity as being 20 m/s, east.

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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 computed using the following equation:

Average speed = distance / time

Units - (m/s)

Meanwhile, the average velocity is often computed using the equation:

velocity (m/s) = displacement (m) time (s)

Constant Speed

An object can move at a steady rate with a constant speed. That is, the object will cover the same distance every regular interval of time. If the speed is constant, then the distance traveled every second is the

same.

Acceleration

Acceleration is a vector quantity which is defined as "the rate at which an object changes its velocity." An object is

accelerating if it is changing its velocity.

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Calculating Acceleration

The acceleration of any object is calculated using the equation:

Acceleration (m/s2) = change in velocity change in time

Acceleration units are m/s 2 .

Direction of the Acceleration Vector

Acceleration is a vector quantity so it will always have a direction

associated with it. The direction of the acceleration vector depends on two factors:

when the object is speeding up it is given the positive (+)

direction

when the object is slowing down it is given a negative (–) direction

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Describing Motion with Diagrams

Describing Motion with Distance vs. Time Graphs

The Meaning of gradient for a distance - time Graph

The gradient of a distance vs. time

graph reveals velocity. For example, a small slope means a small velocity;

a constant slope (straight line) means a constant velocity; a changing slope (curved line) means

a changing velocity.( an acceleration).

Note that for the first five seconds, there is a constant velocity.

Note also that during the last

5 seconds (5 to 10 seconds), the line goes up 0 meters. That is, the velocity is 0 m/s — the

object is stationary.

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Describing Motion with Velocity vs. Time Graphs

The Meaning of Shape for a v-t Graph

Consider a car moving with a constant, rightward (+) velocity of +10 m/s. A car moving with a

constant velocity is a car moving with zero acceleration.This

results in a line of zero dradient when plotted as a velocity-time graph.

Now consider a car moving with a

rightward (+), changing velocity – that is, a car that is moving rightward and speeding up or accelerating.

Note that a motion with changing,

positive velocity results in a diagonal line when plotted as a velocity-time graph. The gradient of this line

corresponds to the acceleration.

Positive Velocity Zero Acceleration Positive Velocity Positive Acceleration

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Acceleration vs. Deceleration

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.

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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 trapeziumd 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.

Graphical Interpretation of Acceleration

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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. Slowing down can

also 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.

Describing Motion with Equations

Form 4 – Unit 2 – Theme 1 – On the Move 9

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 or ms )

speed (m/s) = distance (m) 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

Using the Kinematic Equations

Form 4 – Unit 2 – Theme 1 – On the Move 10

The kinematic 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. They are also called equations of motion.

1.

Speed at finish = speed at start + change in speed

change in speed = acceleration × time.

Speed at end = speed at start + (acceleration × time)

2.

Distance = average speed × time

4.

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The application of these four equations to the motion of an object in free fall can be aided by a proper understanding of the conceptual

characteristics of free fall motion. These concepts are as follows:

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.

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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

are applied to where it comes to rest.

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These are some of the factors that affect how effective your

braking will be:

Brakes : Damaged brakes won't work as well, so you'll

need to brake for longer.

Tyres : Good tyres can reduce braking distance by

many metres! Worn tyres (with little tread) will have

good grip in the dry but in the wet will lead to much

longer braking distances.

Road Surface : Different types of surface provide

different levels of grip, especially in the wet. If the road

is wet, braking distance will always be longer. Oil spills on the road, gravel, etc. all reduce grip and increase

braking distances.

Stopping time is the thinking and braking times added together. The total time to stop a moving vehicle. Stopping

distance is the thinking distance added to the braking

distance.