Find total Distance?

Question

A particle's velocity is modeled by an equation.

To find the total distance traveled by that particle in a certain interval, would i integrate the velocity function? or integrate twice so i'm integrating the position function?

Answer 1

My college physics is rusty, so you may want to verify my answer before accepting it.

If an equation provides the velocity given a variable, say for instance time, then the integral of the velocity equation with respect to this variable gives the position. i.e. v(t)=df(t)/dt, where v is the velocity function, t is time and f(t) is the position function.

To determine the net change in position, the distance over time in this case, you would not integrate again. Instead, you would want to solve f for the end time, t2, and subtract the solution of f for the beginning time: distance = f(t2) - f(t1).

Hope this helps and that my recollection is correct.

Answer 2

If the velocity is changing with respect to time, then you need to integrate the velocity with respect to time to obtain the distance traveled.

Answer 3

If the army of X miles lin length marched X miles, then going from decrease back to front interior the comparable time might require the soldier flow at two times the %. of the army, and he might have travelled a distance of 2x. while the soldier turns decrease back, he's shifting at a destructive cost while in comparison with the army... he's marching backwards two times as quickly as they are shifting forward, so his internet cost relative to the army is 2X + x = 3X for this reason, interior the time he marches backwards to fulfill the rear, the army might have moved a distance of a million/3X, and he might have flow 2/3 X. So, the respond may well be 2x + 2/3 x = 2.66X

Answer 4

Using the equation for velocity you would integrate once. You would integrate twice if you had an equation for acceleration.

Hope this helps! :)

Answer 5

Distance = integral (dv/dt).