# Unit 2: Section 2 Space, Time and Motion

Unit 2; Section 2 Space, Time and Motion

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• Created by: R_Hall
• Created on: 09-05-13 20:49

## Scalars and Vectors

• Scalars have no direction. just an amount (eg. mass, speed, energy, time)
• Vectors have displacement and magnitude (eg. displacement, velocity, acceleration, force)
• Adding two or more vectors- finding the resultant. Add by drawing tip-to-tail
• Resultant vectors can be split into two components at right angles to each other- horizontal and vertical components
• Horizontal and vertical components are separate and independent of each other
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## Motion with Constant Acceleration

• Acceleration is the rate of change of velocity
• There are 4 main equations for solving problems involving uniform velocity
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## Free Fall and Projectile Motion

• Acceleration is a vector quantity- and acts as 'g' vertically downwards. g= 9.81 ms-2.
• The only force acting on an object in free fall is its weight
• Objects can have an initial velocity in any direction and still undergo free fall as long as the force providing initial velocity is no longer acting
• G is always downwards, so is usually a negative value
• If somethings projected at an angle, you start with both horizontal and vertical velocity
• 1. Resolves initial velocity in both components
• 2. Use vertical to work out how long in air and/or how high it goes
• 3. Use horizontal to work out how far it goes
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## Displacement-Time Graphs

• A graph of displacement against time for an accelerating object always produces a curve
• If the object is accelerating at a uniform rate, then the rate of change of the gradient will be constant- a straight line
• The gradient on a displacement-time graph gives the velocity
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## Velocity-Time Graphs

• Acceleration is the gradient of a velocity-time graph. Uniform acceleration is a straight line; the steeper the gradient, the greater the acceleration
• The distance travelled is the area under a speed-time graph
• Non-uniform acceleration is a curve on a v-t graph- increasing acceleration is an increasing gradient, decreasing acceleration is a decreasing gradient
• A data-logger can be to automatically record distance of an object from a sensor several times a second. Attaching it to graph-drawing software allows you to get real time d-t and v-t graphs
• Main advantages- more accurate data, higher sampling rate and data can be displayed in real time
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## Forces

• If a body is in equilibrium (not accelerating), the forces acting are balanced
• To resolve a force, you should split into components and use trigonometry
• If two forces act on an object, find the resultant by adding the vectors into a closed triangle, and the third side represents the resultant
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## Forces and Acceleration

• If no resultant force acts on an object, its velocity will not change
• When you change something's velocity, you either change speed, direction or both
• Resultant force (N)= mass (kg) x acceleration (ms-2) OR F= ma
• The more force on a mass, the more acceleration
• The more mass, the less acceleration
• If there is no resultant force, the acceleration must be 0
• The force that causes objects to accelerate towards the ground is the gravitational pull. G is constant, so all objects should accelerate towards earth at the same rate, regardless of mass
• Acceleration is independent of the mass
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## Work and Power

• You need force to move something because you have to overcome another force. The moving object has kinetic energy during the move, and this energy is transferred to another form when it stops
• Work is the amount of energy transferred. W= F x s
• The equation assumes force is in the same direction as movement. If this isn't the case, trigonometry is used to find the horizontal and vertical components
• Power is the rate of doing work- the amount of energy transformed from one form to another per second. P= W/t
• Power also = F x v
• If force and motion are in different directions, you can replace F with Fcos0 to get P=Fv cos0
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## Conservation of Energy

• Energy cannot be created or destroyed. It can be transferred from one form to another, but the total amount of energy in a closed system will not change
• Kinetic energy is the energy of anything moving
• Gravitational potential energy is the energy something gains when you lift it up
• Elastic potential energy is the energy you get in a stretched rubber band or spring, for example
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