Question

The velocity of an object (in meters per second) is given by the differential equation ds/dt=-0.2s,where s is the object’s position from the origin at time t. If the initial position of the object is 5 meters from the origin, find its position after 10 seconds.


0.135 meters
0.677 meters
4.323 meteres
4.865 meters

Answer 1

First, do you know how to solve the differential equation \[\frac{ds}{dt} = -0.2s \]

Once you have a solution, use your initial condition of \(s =5\) at \(t = 0\) to find the value of the constant introduced while solving the ODE, then substitute \(t=10\) to find the position.