Variable acceleration in stages and velocity as a function of time
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 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
- When the rule changes
- Velocity as a function of time
- Acceleration is zero
Read the transcript of the teaching part
Last time
Before we start: last time, in Acceleration and displacement as functions of time, and displacement-time graphs, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
When the rule changes
Sometimes one formula cannot describe the whole journey. The velocity follows one rule for the first ten seconds, then switches to another. You must treat each stage separately. And whenever velocity changes sign, distance and displacement part company.
Velocity as a function of time
Given v as a formula in t, acceleration is the derivative of v. Zero acceleration means a stationary point of v. Displacement is the integral of v. The area under the v t graph, with sign. Distance is the total ignoring direction, so split the integral wherever v changes sign.
Acceleration is zero
Take v equals 2 t squared minus 6 t minus 3. Differentiate: a equals 4 t minus 6. Acceleration is zero when 4 t equals 6, so t is 1.5 seconds.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Acceleration as a function of time · Variable acceleration in stages · Velocity as a function of time.
The whole chapter: Kinematics.
Chapter 4.2: Kinematics of motion in a straight line
- Constant acceleration, vertical motion and velocity-time graphs 5 min
- Acceleration and displacement as functions of time, and displacement-time graphs 6 min
- Variable acceleration in stages and velocity as a function of time 6 min
- Two particles: gravity, a track, successive intervals and mid-air collisions 7 min
Also for A Level Maths 9709 Paper 4
Which topics come up most in A Level Maths 9709 Paper 4 past papers, counted from every paper since 2004.