Kinematics: displacement, velocity, acceleration and graphs
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Three quantities, one chain
- The chain
- Speed, velocity and distance
Read the transcript of the teaching part
Last time
Before we start: last time, in Definite integrals and plane areas, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Three quantities, one chain
Where is the particle? How fast is it moving? How quickly is its speed changing? Those are displacement, velocity and acceleration. Each one is the rate of change of the one before. So calculus links them all, and a velocity graph holds the whole story.
The chain
Velocity is the rate of change of displacement: v equals ds by dt. Acceleration is the rate of change of velocity: a equals dv by dt, which is d two s by dt squared. Going the other way, integrate. Velocity integrates to displacement, and acceleration to velocity. Remember the constant of integration, which you find from the starting conditions.
Speed, velocity and distance
Velocity can be negative, meaning motion in the negative direction. Speed is its size, always positive. Displacement is the position from the fixed point. Distance travelled is the total length of path. If the particle turns round, the distance is the sum of the separate stretches.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Displacement, velocity and acceleration · Kinematics graphs.
The whole chapter: Kinematics.
Chapter 14: Differentiation and integration
- Differentiation: standard functions, chain, product and quotient rules 5 min
- Tangents and normals 5 min
- Stationary points and the derivative tests 5 min
- Practical maxima and minima 5 min
- Connected rates of change and small increments 5 min
- Integration: powers of x and the reverse of differentiation 5 min
- Integrating (ax + b)ⁿ, exponentials and trigonometric functions 5 min
- Definite integrals and plane areas 5 min
- Kinematics: displacement, velocity, acceleration and graphs 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.