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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