This problem requires us to find the velocity function and evaluate its magnitude after a very long time given a force function.
This is a Force with Calculus type of problem since we have the force as a function of time. We'll follow these steps:
A diagram like this one can help you remember the relationships between the variables:
In step 2, we need to recall how to integrate an exponential.
, where C is the constant of integration.
The velocity function is the integral of the acceleration function, a(t). We're not given a(t), but we are given a function for force, F(t).
So here's our process:
At t = 0, an object of mass m is at rest at x = 0 on a horizontal, frictionless surface. Starting at t = 0, a horizontal force Fx = F0e−t/T is exerted on the object.
(a) Find an expression for the object's velocity at an arbitrary later time t.
(b) What is the object's velocity after a very long time has elapsed?￼
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Forces with Calculus concept. You can view video lessons to learn Forces with Calculus. Or if you need more Forces with Calculus practice, you can also practice Forces with Calculus practice problems.
What professor is this problem relevant for?
Based on our data, we think this problem is relevant for Professor Wallace's class at UNC.