Help with work and vector forces

mardi 29 octobre 2013

1. The problem statement, all variables and given/known data

A particle of mass 1 kg moves under the force F = 5i + 15t^2j N, where t is in seconds. The initial velocity of the particle is 2i + 3j + 4k ms^−1. Find the work done by the force acting on the particle, and the increase in kinetic energy of the particle , during the time 0 ≤ t ≤ 1.

2. Relevant equations

F=ma or F=m(dv/dt)?

3. The attempt at a solution

i attempted to use the F=m(dv/dt) and put it equal to the force,

so 1(dv/dt)=5i+15t^2, then i integrated to get dx/dt=5ti+15/3*t^3,

I then added the initial velocity of 2i+3j+4k, so now had 5ti+15/3*t^3 +2i+3j+4k,

now i am thinking this is wrong, but my next plan was to integrate this again, with the limits of 0 to 1?

am i on the right track?

Thanks!