This problem requires us to find the velocity and position functions of an object 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:
Remember the power rule of integration.
, 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).
The object's position function, x(t), is the integral of the velocity function v(t).
So here's our process:
A particle of mass m, initially at rest at x = 0, is accelerated by a force that increases in time as F = Ct2.
(a) Determine its velocity as a function of time.
(b) Determine its position as a function of time.
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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.