.A train starts from rest at a station and after 30 seconds stops at the next station, 500m away.
If distance travelled in time T is given by, s = cT^2(k-T) where c and k are constants...
i) Find formulae for velocity and acceleration.
v=s/t so, = cT(k-T) ???
s = ckT^2 - cT^3
v = s' = 2ckT - 3cT^2 = cT(2k - 3T)
s=ut + 1/2at^2 ... this equation only works if acceleration is a constant
cT^2(k-T)=0 + 1/2at^2
a = v' = 2ck - 6cT = 2c(k - 3T)
now, recalculate the following ...
ii)Use the fact that velocity is zero when T=30 to find value of k.
iii)Use the fact that s=500 when T=30 to find c.