Question

At time, t, in seconds, your velocity, v, in meters/second, is given by v(t)=6+(t^2), 0 (=)t(=)6. Use (delta)t= 2 to estimate the distance traveled during this time.
Find the upper and lower estimates, and then average the two. find the upper estimate of distance traveled, find the lower estimate of distance traveled, and find the average.

Answer 1

Answer:

Total distance is 8 meters.

Step-by-step explanation:

First, let's take the equation and analyse it:

v(t) = 6 + t²

The delta t = 2

To find the acceleration, we need to differentiate v with respect to t like this:

dv/dt = d/dt (6 + t²)

         = 2t

At t = 2, the change in velocity (dv/dt) = 2×2 = 4 m/s². This is the acceleration,a

The final velocity is given by v = 6 + (2)²

                                                   = 10 m/s

The distance is given by the formula:

s = ut + 1/2at²

initial velocity, u = 0

Therefore, the equation becomes s = 1/2at²

                                                            = 1/2× 4×4

                                                             = 8 m Ans