AS Level Further Mechanics 1+2

Sum to infinity to find total vertical distance travelled

Sum to infinity to find total vertical distance travelled

where a1 = initial height and r = ratio of change in height after each bounce (typically e²)

Integration by parts formula

Choose dv as whichever term is easier to integrate

Kinematics rules

s → v → a

Differentiate forwards

Integrate backwards (with respect to time)

Finding time taken for one whole revolution

Time = Distance / (angular) speed

2pi/w = 2pir/v

How to know when to use substitution or parts