Calculus Help :) (1 Viewer)

[madbandlt]

A particle is brought to top speed with an acceleration which varies linearly as the distance travelled. It starts from rest with an acceleration of 3ms^-2 and reaches top speed in a distance of 160 metres.

Find:

(a) the top speed,

(b) the speed when the particle has moved 80 metres



Thanks in Advance!!

 

[cutemouse]

A particle is brought to top speed with an acceleration which varies linearly as the distance travelled. It starts from rest with an acceleration of 3ms^-2 and reaches top speed in a distance of 160 metres.

Find:

(a) the top speed,

(b) the speed when the particle has moved 80 metres



Thanks in Advance!!

a=kx, for k constant.

When t=0, a=3 and x=160
3=160k
k= 3/160

Now a=d/dx(1/2 v^2)

so 1/2 v^2=3x^2/320 + c

When t=0, v=0, x=0

So c=0

so v^2= 3x^2/160

etc I'll complete later if someone already hasn't.