Mathematics differntial equations (acceleration)

[delsoo]

Homework Statement

part b (question 1 ) , my ans is -3/2 ... but the ans given is 2/3... i don't know where's my mistake...
http://imgur.com/ZCrnKA8,bu5bblS
http://imgur.com/ZCrnKA8,bu5bblS#1 thanks in advance!

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

you were given a(t)=3t²-10t
you put dv/dt = a(t) and solved the initial value problem to find v(t) and thus v(2).

in the next part you did fine up to: v.dv = a(t).dx but you cannot take a(t) outside the integration.
since x changes with t, t must be a function of x.

instead: since you have v(t) already:
consider: what is the relationship between v(t) and x(t)?

 

[Simon Bridge]

How did you get on?