Calculating Time Taken for Particle to Travel from x=1 to x=8

[madglover]

Homework Statement

Express the time taken for the particle to travel from x=1 to x=8 as a definate integral with respect to x.

Homework Equations

A particle P moves under the influence of a force

F(x)= (16/x^2) -2

The Attempt at a Solution

first i worked out V(x), such that V(x)=- the integral of F(x)

V(x) = 2x +16/x + a constant

we are then told P is released from rest at x=1

so we can obtain V(1)=0=2+16-C
C=-18

so V(x)=2x +16/x -18

V(x) is the potential function btw

so we can work out the particle is bounded by x=1 and x=8


I'm just not sure how to express the time as an integral in terms of x. we haven't done much like that.

 

[kurt.physics]

i thought it would involve expressing the velocity as an integral and then integrating again to obtain a formula for t, but i was not sure how to do this. any help would be great!