S v t t Gradient of ST graph = Gradient of a VT graph = Area under a VT graph = Velocity Acceleration Displacement

Variable Acceleration Know how displacement, velocity, and acceleration are linked by calculus Understand how to use calculus to find equations Be able to add something here... It’s alright Kim, no one reads this. Hey, Kim isn’t even your name.

General Motion When acceleration is not constant we can use calculus to help use link a, v and s We can differentiate when we would have considered gradients We can integrate when we would have considered areas. To use this method you need an equation as a function of time.

Differentiation Example: s = 3t5 + 2t3 + t + 5 find v and a when t = 1

Integration If a = f(t) If v = g(t) Example: a = 2t3 + 6 find the change in velocity between t =0 and t = 2

Displacement Differentiate Velocity Integrate Acceleration

A particle moves in a straight line A particle moves in a straight line. Its velocity t s after leaving a fixed point on the line is v ms-1 where v = t + 0.1t2. Find an expression for the acceleration of the particle at time t and the distance travelled by the particle from time t = 0 until the instant when its acceleration is 2.8ms-2.

Some solutions require double diff. or integration Puzzle Time Some solutions require double diff. or integration

Calculus Techniques Required You will be required to use ideas from C3 also.

Independent Study Exercise A p 46 (solutions p 153)