How Does Constant Power Affect Truck Acceleration and Position?

[nns91]

SUPER URGENT ! Power question

Homework Statement

A truck of mass m is accelerated from rest at t=0 with constant power P along a level road

show that the position of the truck is related to its speed by x=(m/3P)v^3

the position of the truck is previously found as:

x=(8P/9m)^1/2*t^3/2

I also found the v=(2P/m)^1/2*t^1/2

Homework Equations

Integral

The Attempt at a Solution

I have not found anyway to do this problem yet. I tried to to relate v to x by taking the integral of v by integrate (m/3P)v^3 but I am stuck.

 

[tiny-tim]

Hi nns91!

… show that the position of the truck is related to its speed by x=(m/3P)v^3

the position of the truck is previously found as:

x=(8P/9m)^1/2*t^3/2

I also found the v=(2P/m)^1/2*t^1/2

erm … i think you need a power nap …

if v=(2P/m)^1/2*t^1/2,

then v³ = … ?