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Kinematics (Edexcel IGCSE Maths)
Revision Note
What does kinematics mean?
- Kinematics is the study of the motion of a particle (object) linking the three vector quantities displacement, velocity and acceleration
- Motion is in a straight line – think of the particle as moving along a number line
- The number line has a fixed point O (the origin)
- The number line has both negative and positive values
- The particle can move in both directions along the number line
- Note that in kinematics, a particle is an object – it could be a football, a car, a train - anything that has motion. A particle is modelled as taking up a single point in space
What is displacement and how is it different to distance?
- Displacement measures how far the particle is from the origin and is a vector quantity, so it can be negative
- Distance is always positive
- Displacement is measured from the fixed point O
- The letter s is used for displacement
- It is usually measured in metres (m)
- If s = 4 then the distance from the origin is 4 m and the particle is 4 m “in front of” the origin
- If s =-5 then the distance from the origin is 5 m and the particle is 5 m “behind” the origin
- The + or - indicates the particle’s position relative to the origin
- Displacement is a function of time, t, where time is usually measured in seconds
- eg. s = 3t3 - 2t + 1
At time t = 0, s = 1
At time t = 2, s = 21
- eg. s = 3t3 - 2t + 1
At time t = 0, s = 1
What is velocity and how is it different to speed?
- Velocity measures how fast the particle is travelling and is a vector quantity, so it can be negative
- Speed is always positive
- The letter v is used for velocity
- It is usually measured in metres per second (m/s)
- If v = 3 then the speed of the particle is 3 m/s and it is moving in the positive direction
- If v = -6 then the speed of the particle is 6 m/s and it is moving in the negative direction
- The + or - indicates the particle’s direction of motion
- Velocity is a function of time, t, and is the rate of change of displacement
- To find v, differentiate s, ie.
If s = t3 - 2t2
then = 3t2 – 4t
- To find v, differentiate s, ie.
If s = t3 - 2t2
- If velocity is zero then the particle is stationary (not moving)
What is acceleration?
- Acceleration measures how fast the velocity is change and is a vector quantity, so it can be negative
- The magnitude of acceleration is always positive
- The letter a is used for acceleration
- It is usually measured in metres per square second (m/s2)
- If a = 1 then the magnitude of acceleration is 1 m/s2 and the particle is accelerating (velocity increasing / speeding up)
- If a = -6 then the magnitude of acceleration is 6 m/s2 and the particle is decelerating (velocity decreasing / slowing down)
- The + or - indicates whether the particle is accelerating or decelerating
- Acceleration is a function of time, t, and is the rate of change of velocity
- To find a, differentiate v, ie.
If v = 3t2 – 4t
then = 6t - 4
- To find a, differentiate v, ie.
If v = 3t2 – 4t
- If acceleration is zero then the particle is moving at a constant velocity
How do I solve kinematics problems?
- Be clear about how the three quantities are related through differentiation
- There are some key phrases to look out for
- Initial / initially means when t = 0 (at the start)
- At rest means when v = 0 (not moving, no velocity)
- If the rest is only at one point in time (in an instant) then it is instantaneous rest
- For example, find the value of t for which the particle is at instantaneous rest (solve v = 0 to find t)
Examiner Tip
Displacement, velocity and acceleration can all be negative whereas distance, speed and magnitude of acceleration are always positive.
Worked example
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