The position of an object as a function of time is given as
x = At3 + Bt2 + Ct + D.
The constants are
A = 3.2 m/s3,
B = 1.8 m/s2,
C = −4.2 m/s,
and
D = 7 m.
At what time(s) is the object at rest?
It is at rest when the derivative dX/dt = 0
So solve
9.6t^2 +3.6t -4.2 = 0
which is the same as
16t^2 +6t -7 = 0
This can be factored to give
(2t -1)(8t+7) = 0
They probably want only the solution for which t>0.
2.1
To find the time(s) when the object is at rest, we need to solve for the value(s) of time (t) when the position (x) is equal to zero (0). In other words, we need to solve the equation:
0 = At³ + Bt² + Ct + D
Given the constants A, B, C, and D, let's substitute them into the equation:
0 = 3.2t³ + 1.8t² - 4.2t + 7
Now, we need to solve this equation to find the value(s) of t when x = 0. This equation is a cubic equation, so we can solve it using various methods, such as factoring, graphical methods, or numerical methods like Newton's method.
One possible method to solve this equation is to use numerical methods. Let's use an online calculator or software that can solve cubic equations. There are several options available, such as Wolfram Alpha, Mathway, or online equation solvers.
1. Visit an online cubic equation solver or use a software program that can solve equations.
2. Input the equation: 3.2t³ + 1.8t² - 4.2t + 7 = 0
3. Click on the "Solve" or "Calculate" button to get the solution.
The solver will give you the value(s) of t when the object is at rest. It may provide the solution as a decimal or fraction, depending on the solver used.
Once you have the solution(s) for t, those will be the time(s) at which the object is at rest.