A ball is dropped from rest from a window 3m above ground height. How long will it take the ball to hit the ground? (You may assume air resistance on the ball is negligible.)
This is a very common mechanics question you can be asked in a physics exam (or a M1 maths exam!). The key to solving it is to realise that the ball is in freefall, so it is only acted on by gravity. Since this is a constant force (F=mg), the acceleration of the ball will be constant (a=g). Therefore the "SUVAT" equations (the equations of motion for an object under constant acceleration) may be used to solve this. First, write out everything you know and everything you are trying to find: u = 0 ms-1 (ball dropped from rest), a = g = 9.81 ms-2, s = 3 m, v: ?, t: need to find. Next, look at all the SUVAT equations and figure out which ones are relevant: s = ut + 0.5at2 , v = u + at , s = 0.5(u+v)t and v2 = u2 + 2as.
We need to find t. But we don't know what v is, so we need to find an equation that includes t but not v. s = ut + 0.5at2 clearly works. u = 0, so s = 0.5at2. Rearranging this gives t=(2s/g)0.5 = (2*3/9.81)0.5 = 0.782 s
