Constant acceleration, vertical motion and velocity-time graphs
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 4 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
- Motion in stages
- The constant acceleration equations
- Vertical motion
Read the transcript of the teaching part
Last time
Before we start: last time, in Limiting friction on slopes, connected particles and forces in equilibrium, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Motion in stages
A bus pulls away, cruises, then brakes. Each stage has its own constant acceleration, so you handle them one at a time. And a velocity time graph shows all the stages at once, with the area giving the distance.
The constant acceleration equations
There are five quantities: displacement s, initial velocity u, final velocity v, acceleration a, and time t. v equals u plus a t. And s equals u t plus a half a t squared. v squared equals u squared plus two a s. And s equals a half, bracket u plus v, t. Write down the three known quantities, pick the equation without the one you do not need.
Vertical motion
A particle thrown upwards has acceleration minus g, which is minus ten metres per second squared, taking up as positive. At the greatest height the velocity is zero. This is the key fact for the greatest height. Time up equals time down for a particle returning to its starting level.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Velocity–time graphs · Vertical motion under gravity.
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.