You are pretty much right. f'(t) = 20 - 10t. Plug in t= 6 to get 20 - 60 =-40 m/s. This is the velocity. The speed is the magnitude of the velocity, which is |-40| = 40 m/s.
this has to do with diffrentiation and not kinematics
a boy stands on the edge of a cliff of height 60m. he throws a stone vertically upwards so that its distance h metres above the cliff top is given by h=20t -5(t^2)
a. calculate the max height of the stone above the cliff top
i differentiated h=f(t) and got 20m
b. calculate the time which elapses before the stone hits the beach (it just misses the boy on the way down (lucky him))
i took h=-60 and got t=6
c. calculate the speed with which the stone hits the beach.
here i'm lost. shouldnt speed=f'(t)=20-10t? but i know this is wrong cos the answer is 40ms^-1