This problem requires us to find the position of the object after a force giving it constant acceleration is applied.
This is a Forces 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.
Since we're looking for the object's position, we want to find an expression for x(t), which is the integral of the velocity function v(t). The only information we have about the object's velocity is that it starts from rest, so we need another step, though!
The velocity function is the integral of the acceleration function, a(t). We're not given that, either, but we are given a function for force, F(t). So here's our process:
A mysterious rocket-propelled object of mass 45.5 kg is initially at rest in the middle of the horizontal, frictionless surface of an ice-covered lake. Then a force directed east and with magnitude F(t) = (16.1 N/s)t is applied.
How far does the object travel in the first 5.25 s after the force is applied?
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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.