Calculus in kinematicsAQA A-Level Maths: Flashcards

What these 13 flashcards ask

State the link between displacement and velocity.
State the link between velocity and acceleration.
How do you find displacement from velocity?
How do you find velocity from acceleration?
What does v=0 tell you?
How do you find when the velocity is greatest or least?
Differentiate r=2t^3-9t^2+12t to get v.
Integrate a=6t-4 with v=5 when t=0.
When does distance differ from displacement?
How do you find the total distance with a change of direction?
When can you use v=u+at?
What are the units of r, v and a in SI?
Why is the constant of integration needed?

Exam questions on Calculus in kinematics

A particle moves in a straight line. Its displacement from a fixed point $O$ at time $t$ seconds is $r=2t^3-9t^2+12t$ metres.
Find the values of $t$ at which the particle is instantaneously at rest.2 marks
A particle moves in a straight line. At time $t$ seconds its acceleration is $(6t-4)$ m s⁻². When $t=0$ the particle is at the fixed point $O$ and has velocity $5$ m s⁻¹.
Show that the particle is never instantaneously at rest.2 marks
A particle $P$ moves on a straight line through a fixed point $O$ . At time $t$ seconds, $t\ge0$ , its velocity is $v=3t^2-12t+9$ m s⁻¹. When $t=0$ , $P$ is at $O$ .
Find the acceleration of $P$ at each time when it is instantaneously at rest.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).