In this problem, we are required to determine the function for the force on an object given the position as a time-varying function.
Since we have the position as a function of time, we know this is a calculus problem.
A diagram like this one can help you remember the relationships between the variables:
Since we're looking for the magnitude of the force exerted on the object, we'll have to find an expression for acceleration, a(t). The a(t) function is obtained by differentiating the position function, x(t), twice. Then, we'll multiply the a(t) function by the mass, m, to get the force expression.
The steps needed to solve this problem are simple and straight forward:
In Step 1, we'll need to remember the power rule of differentiation:
An object with mass m moves along the x-axis. Its position as a function of time is given by x(t)=At - Bt3, where A and B are constants.
Find an expression for the x-component of the force acting on the object as a function of time.
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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. If you need more Forces with Calculus practice, you can also practice Forces with Calculus practice problems.