# P9 Motion

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## 9.1 Speed and distance-time graphs

• Constant speed means the same amount of time to go to the next distance.
• The gradient on a distance-time graph means speed. The steeper it is, the faster it is.
• (average) speed, v (m/s) = distance, s (m)/time, t (s)
• Long distance vehicles have tachographs which make sure drivers don't drive for too long.
• If the object travels the furthest distance in the same time, it is the fastest.
• A smaller gradient means it is going slower (for a distance-time graph).
• A flat line means it is stationary (for a distance-time graph).
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## 9.2 Velocity and Acceleration

• Velocity is speed in a given direction. You can have the same speed but different velocities. An object moving around in a circle has a direction of motion changing continuously whilst it goes around: the velocity isn't constant even if the speed is constant.
• Displacement is distance travelled in a given direction.
• Acceleration is the change of velocity per second.
• acceleration = change in velocity (m/s^2)/time, t (s) or
a= v-u/t
(v is in the final velocity and u is the initial velocity)
• Deceleration is when the object slows down.
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## 9.3 More about velocity time graphs

• A motion sensor linked to a computer records how velocity changes and displays measurements as a graph.
• In acceleration, velocity increases with time.
• On a velocity-time graph, a straight line is constant acceleration.
• On a velocity-time graph, a steeper gradient is faster.
• On a velocity-time graph, the gradient represents acceleration.
• Braking reduces velocity and velocity is constant until the brake is applied.
• On a velocity-time graph, a flat line is constant velocity and a gradient of 0 means 0 acceleration.
• The area under the line on a velocity-time graph is displacement. To work out the area, the area of a triangle is 1/2bh and a square is lw. It could be made of compound shapes.
• If the speed or velocity is in km/h, convert to metres.
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## 9.4 Analysing motion graphs

• On a distance-time graph, the speed of an object is the gradient of the line. If it is a straight line, draw a triangle underneath the line. The height is distance travelled and the base is the time. Work out the gradient by height/base.
• For a moving object with changing speed (a curved line), draw a tangent at the point and then do height/base.
• A straight line and constant gradient mean constant acceleration.
• Equation:
acceleration = change in velocity/time taken
• If time is not given and there is constant acceleration, use:
v^2-u^2=2as
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## Required Equations

• Distance travelled(m) = speed (m/s) x time (s)
s = vt
• Acceleration(m/s^2) = change in velocity(m/s)/time taken(s)
a = Δv/t
• Uniform Acceleration:
Final velocity(m/s) - Initial velocity(m/s) = 2 x Acceleration(m/s^2) x Distance(m)
v^2-u^2=2as
• Resultant force(N) = Mass(kg) x Acceleration(m/s^2)
F = ma
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