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Velocity and Acceleration
Speed and velocity are similar, but in physics they’re not quite the same…
Speed and Velocity are both how fast you’re going
Both have units of m/s.
Speed is just how fast you’re going (e.g. 30 mph or 20 m/s) with no regard for
Velocity however must also have the direction specified, e.g. 30 mph north or 20
m/s, 060º.
1) This means you can have objects travelling at a constant speed with a changing
velocity. This happens when the object is changing direction whilst staying at the
same speed.
2) For any object, the distance moved, (average) speed, and time taken are related to this
π‘¨π’—π’†π’“π’‚π’ˆπ’† 𝒔𝒑𝒆𝒆𝒅 =
π‘«π’Šπ’”π’•π’‚π’π’„π’† π’Žπ’π’—π’†π’…
π‘»π’Šπ’Žπ’† π’•π’‚π’Œπ’†π’
Example: A cat walks 20 m in 35 s. Find: a) its average speed. b) how long it takes to walk
75 m.
Using the formula triangle:
a) 𝒗 = 𝒔⁄𝒕 = 𝟐𝟎⁄πŸ‘πŸ“ = 𝟎. πŸ“πŸ• π’Ž/𝒔
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b) 𝒕 = 𝒔⁄𝒗 = πŸ•πŸ“⁄𝟎. πŸ“πŸ• = πŸπŸ‘πŸ 𝒔 = 𝟐 π’Žπ’Šπ’ πŸπŸπ’”
1) Acceleration is not the same as velocity or speed. Acceleration is how quickly the
velocity is changing.
2) This change in velocity can be A CHANGE IN SPEED or CHANGE IN
DIRECTION or both. You only need to worry about the change in speed for
3) The unit of acceleration is π’Ž⁄π’”πŸ .
4) There are two formulas you need to know:
π‘¨π’„π’„π’†π’π’†π’“π’‚π’•π’Šπ’π’ =
π‘ͺπ’‰π’‚π’π’ˆπ’† π’Šπ’ π’—π’†π’π’π’„π’Šπ’•π’š
π‘»π’Šπ’Žπ’† π’•π’‚π’Œπ’†π’
• (V – U) is change in velocity rather than just velocity.
Example: The cat accelerates from 2 π‘š⁄𝑠 to 6 π‘š⁄𝑠 in 5.6 s. Find its acceleration.
Using the formula triangle:
( 𝒗−𝒖)
π’—πŸ = π’–πŸ + πŸπ’‚π’”
= 𝟎. πŸ•πŸ π’Ž⁄π’”πŸ
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A van travelling at 23 π‘š⁄𝑠 starts decelerating uniformly at 2.0 π‘š⁄𝑠 2 as it heads
towards a built – up area 112 m away. What will its speed be when it reaches the built-up
1) Put the numbers in – remember “a” is negative. Because its deceleration.
𝑉 2 = π‘ˆ 2 + 2π‘Žπ‘ 
𝑉 2 = 232 + (2 × −2.0 × 112) = 81
2) Finally, square root the whole thing.
𝑉 = √81 = 9 π‘š⁄𝑠
Distance-Time and Velocity-Time Graphs
Make sure you can distinguish between the two properly.
The different parts of a distance time graph describe the motion of an object:
The gradient (slope) at any point gives the speed of the object.
Flat sections are where its stopped.
A steeper graph means it’s going faster.
Curves represent acceleration.
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A curve getting steeper means its speeding up (Increasing gradient).
A levelling off curve means it’s slowing down. (Decreasing gradient)
You can calculate the average speed of an object over a period of time by dividing the
total distance travelled by the time it takes to travel the whole distance.
For example, the average speed over the whole journey is
= 6.25 π‘š⁄𝑠
How an object’s velocity changes over time can be plotted on a velocity-time graph.
Gradient = Acceleration.
Flat sections represent steady speed.
The steeper the graph, the greater the acceleration or deceleration.
Uphill sections (/) are acceleration.
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Downhill sections (\) are deceleration.
The area under any part of the graph is equal to the distance travelled in that time
A curve means changing acceleration.
Mass, Weight and Gravity
Gravity attracts all masses, but you only notice it when one of the masses is really big. e.g.,
a planet. Anything near a planet or star is attracted to it very strongly.
This has three important effects:
1) On the surface of a planet, it makes all
things accelerate towards the ground (all
with the same acceleration, g, which is
about 10 π‘š⁄𝑠 2 on Earth).
2) It gives everything a weight.
3) It keeps planets, moons and satellite in
their orbits. The orbit is a balance between
the forward motion of the object and the
force of the gravity pulling it inwards.
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To understand this, you must learn all these facts about mass and weight:
1) Mass is just the amount of “stuff” in an object. For any object this will have the
same value anywhere in the universe.
2) Weight is caused by the pull of gravity. In most questions the weight of an object is
just the force of gravity pulling it towards the centre of the Earth.
3) An object has the same mass whether its on the Earth or on the Moon – but it’s
weight will be different. A 1 Kg mass will weigh less on the Moon (about 1.6 N) that
it does on Earth (about 10 N), simply because the force of gravity pulling it on it
4) Weight is a force measured in Newtons. It’s measured using a spring balance or
newton meter. Mass is not a force. It’s measured in kilograms with a mass balance.
π‘Ύπ’†π’Šπ’ˆπ’‰π’• = π’Žπ’‚π’”π’” × π’ˆπ’“π’‚π’—π’Šπ’•π’‚π’•π’Šπ’π’π’‚π’ π’‡π’Šπ’†π’π’… π’”π’•π’“π’†π’π’ˆπ’•π’‰
𝑾=π’Ž ×π’ˆ
1) Mass and weight are not the same, mass is in kilograms and weight is in newtons.
2) The letter “g” represents the strength of the gravity and its value is different for
different planets. On Earth, g = 9.81 𝑁⁄π‘˜π‘”. On the moon, g = 1.6 𝑁⁄π‘˜π‘”.
Example: What is the weight in Newtons, of a 5 kg mass, both on Earth and on the moon?
Using the formula, π‘Š = π‘š × π‘”.
On Earth: π‘Š = 5 × 9.81 = 49.05 𝑁
On Moon: π‘Š = 5 × 1.6 = 8 𝑁
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Forces and Friction
A force is simply a push or a pull. There are lots of different types of forces you need to
know about:
GRAVITY or WEIGHT – close to a planet this acts straight downwards.
REACTION FORCE – acts perpendicular to a surface and away from it.
ELECTROSTATIC FORCE – between two charged objects. The direction depends
on the type of charge (like charges repel, opposite charges attract)
THRUST – e.g. PUSH or PULL due to an engine or rocket speeding something up.
DRAG or AIR RESISTANCE or FRICTION which is slowing the thing down.
LIFT – e.g. due to an aeroplane wing
TENSION in a rope or cable.
1) There are lots of forces acting on you right now, but you don’t feel them because they
balance out.
2) Any object with a weight will feel a reaction force back from the surface its on.
Otherwise, it would just keep falling.
3) When an object moves in a fluid (air, water, etc). it feels drag in the opposite
direction to its motion.
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1) If an object has no force propelling it along, it always slows down and stop because
of friction. Friction is force that opposes motion.
2) To travel at a speedy speed, things always need a driving force to counteract the
3) Friction occurs in three main ways:
a) Friction Between Solids Surfaces Which Are Gripping.
b) Friction Between Solid Surfaces Which Are Sliding Past Each Other
You can reduce both these type of friction by putting a lubricant like oil or grease between
the surface. Friction between solids can often cause wear of the two surfaces in contact.
c) Resistance or “drag” from the fluids (liquids or gases, e.g. air)
The most important factor in reducing drag in fluids is keeping the shape of the object
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Investigating Motion – Practical
1) Set up your apparatus like in the diagram below, holding the car still just before the
first light gate.
2) Mark a line on the ramp – this is to make sure the car starts from the same point each
3) Measure the distance between each light gate – you’ll need this to find the car’s
average speed.
4) Let go of the car just before the light gate so that it starts to roll down the slope.
5) The light gates should be connected to a computer. When the car passes through each
light gate, a beam of light is broken and a time is recorded by data-logging
6) Repeat this experiment several times and get an average time it takes for the car to
reach each light gate.
7) Using these times and the distances between light gates you can find the average
speed of the car on the ramp and the average speed of the car on the runway. – just
divide the distance between the light gates by the average time taken for the car to
travel between the gates.