A small 8.00-kg rocket burns fuel that exerts a time-varying upwa...

Question

A small 8.00-kg rocket burns fuel that exerts a time-varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation F = A + Bt2. Measurements show that at t = 0, the force is 100.0 N, and at the end of the first 2.00 s, it is 150.0 N. (a) Find the constants A and B, including their SI units

Accepted Answer

Hey everyone today, we're dealing with a problem regarding forces. Now, at first glance, this looks to be a pretty lengthy problem. We have a formula. We have a bunch of different data sets, right? But um let's take a step back. Just sort of analyze this. So we're given a few key specific parts of info. We have a, excuse me, We have a spacecraft with a massive 12 kg. The forces acting upon the spacecraft obey relations. Such that F at specific time is equal to a plus B, times times squared. Now, at different instants of time, The acceleration is measured, or rather the force at that time is measured. So at time zero we have a force of 60 newtons and at time 2.6 seconds We have a force of 112 newtons. So with this we're being asked to determine the values of both A and B and S. I. Units. Now, let's go ahead and work through this. So let's start off very simply we have our we have our formula or relation which states that if a time T is equal to a plus B T squared, So at time is equal to zero when T is equal to zero seconds, F is equal to 60 Newtons. So substituting that in, we get 16 newtons is equal to a plus B into zero. So this will automatically become zero and we're left with a is equal to 16 newtons. So that is our first part. That is the value of A. But to find out the value of B, we need to use this newly acquired value of A. Again using the second set of instantaneous uh force and time. So let me write this in blue. We have F. Of T equal to A plus B into T squared. And we know that at time is equal to 2.60 seconds f is equal to 112 Newtons. And we know that A. Is 16 newtons. So substituting these values, you go 112 newtons is equal to Eaton's plus B into T squared. And now T squared is 2.6 seconds squared. So This means we have newtons is equal to 6.76 seconds squared into B. And therefore B is equal to 52 newtons divided by 6.76 seconds squared, which is equal to 7.69 newtons per second squared. So that is our answer A has a value of 60 newtons and B has a value of six points or 7.69 newtons per second squared. In other words, it is answer choice. Excuse me, it is an answer choice. D. I hope this helps. And I look forward to seeing you all in the next one

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