Answer:
a.
b.
c.
Explanation:
Modeling With Functions
Careful measurements have produced a model of one sprinter's velocity at a given t, and it's is given by
For Carl Lewis's run at the 1987 World Championships, the values of a and b are
Please note we changed the value of b to negative to make the model have sense. Thus, the equation for the velocity is
a. What was Lewis's acceleration at t = 0 s, 2.00 s, and 4.00 s?
To compute the accelerations, we must find the function for a as the derivative of v
For t=0
For t=2
b. Find an expression for the distance traveled at time t.
The distance is the integral of the velocity, thus
To find the value of C, we set X(0)=0, the sprinter starts from the origin of coordinates
Solving for C
Now we complete the equation for the distance
c. Find the time Lewis needed to sprint 100.0 m.
The equation for the distance cannot be solved by algebraic procedures, but we can use approximations until we find a close value.
We are required to find the time at which the distance is 100 m, thus
Rearranging
We define an auxiliary function f(t) to help us find the value of t.
Let's try for t=9 sec
Now with t=9.9 sec
That was a real close guess. One more to be sure for t=10 sec
The change of sign tells us we are close enough to the solution. We choose the time that produces a smaller magnitude for f(t).