We will see that for t = 3 seconds the object will be at rest.
When does an object is at rest?
We say that something is at rest if its velocity is equal to zero.
Here we know that the position equation of the object is:
x(t) = 7 + 6*t - t^2
To get the velocity, we need to differentiate with respect to the time, using the rule:
[tex]f(x) = a*x^n\\\\f'(x) = n*a*x^{n-1}[/tex]
We will get:
v(t) = 6 - 2*t
Now we just need to find the value of t such that the above equation is equal to zero:
0 = 6 - 2*t
2*t = 6
t = 6/2 = 3
Then for t = 3 seconds, the object will be at rest.
If you want to learn more about motion equations, you can read:
https://brainly.com/question/19365526
