# Finding time given accelration & velocity

• Jul 29th 2010, 11:23 AM
delicate_tears
Finding time given accelration & velocity
A particle travels horizontally with a retardation of v^2/250 m/s^2 when its speed is v m/s. find the interval of time over which its speed drops from 1000 to 500 m/s.
• Jul 29th 2010, 12:17 PM
skeeter
Quote:

Originally Posted by delicate_tears
A particle travels horizontally with a retardation of v^2/250 m/s^2 when its speed is v m/s. find the interval of time over which its speed drops from 1000 to 500 m/s.

$\displaystyle \frac{dv}{dt} = -\frac{v^2}{250}$

separate variables and solve the differential equation using the initial condition $v(0) = 1000 \, m/s$ to get velocity as a function of time.