# Thread: Maths Mechanics SUVAT mechanics

1. ## Maths Mechanics SUVAT mechanics

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.

velocity:
v=s/t so, = cT(k-T) ???

acceleration:
s=ut + 1/2at^2
cT^2(k-T)=0 + 1/2at^2
a=2c(k-T) ???

ii)Use the fact that velocity is zero when T=30 to find value of k.
v=30c(k-30)=0
30ck=900c
k=30

iii)Use the fact that s=500 when T=30 to find c.

The problem here is the (k-T) part of every formula, where k and T are both 30, giving 0... suggesting that k shouldn't be 30?

(not sure what forum to post this in)
Any and all help is greatly appreciated! Many thanks.

2. Originally Posted by fbird67
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.

velocity:
v=s/t so, = cT(k-T) ???

s = ckT^2 - cT^3

v = s' = 2ckT - 3cT^2
= cT(2k - 3T)

acceleration:
s=ut + 1/2at^2 ... this equation only works if acceleration is a constant
cT^2(k-T)=0 + 1/2at^2
a=2c(k-T) ???

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.
.

3. Ah, OK. Thanks a lot, that was a great help.