Question

(1 point) Your velocity is given by v(t)=2t2+8 in m/sec, with t in seconds. Estimate the distance, s, traveled between t=0 and t=8. Use the average of the left and right sums with 4 subdivisions.

Answer 1

Answer:

The estimated distance is 405 meter.

Step-by-step explanation:

Given : Your velocity is given by $v(t)=2t^2+8$ in m/sec, with t in seconds.

To find : Estimate the distance, s, traveled between t=0 and t=8 ?

Solution :

We have to integrate the function from 0 to 8 to get the distance.

Integrate $v(t)=2t^2+8$ w.r.t  t,

$\int\limits^8_0 {2t^2+8} \, dt$

We know, $\int\limits {x} \, dx=\frac{x^2}{2}$

$=[\frac{2t^3}{3}+8t]^8_0$

$=(\frac{2(8)^3}{3}+8(8))-(\frac{2(0)^3}{3}+8(0))$

$=(\frac{1024}{3}+64)-(\frac{0}{3}+8(0))$

$=\frac{1024+192}{3}$

$=\frac{1216}{3}$

$=405.33$

The estimated distance is 405 meter.

Answer 2

The velocity function, v(t) = 2•t² + 8, over the time of t = 0, and t = 8, gives;

• The distance traveled, s is approximately 416 meters

How can the average distance traveled be found?

The given function is; v(t) = 2•t² + 8

Where;

v is the velocity, in m/sec

t is the time in seconds

The width of each rectangle is therefore;

(8 - 0) ÷ 4 = 2

Using the left sums, we have;

A ≈ 2×v(0) + 2×v(2) + 2×v(4) + 2×v(6)

Which gives;

A ≈ 2×8 + 2×16 + 2×40 + 2×80 = 288

Using the right sums, we have;

A ≈ 2×16 + 2×40 + 2×80 + 2×136 = 544

The average of the left and right sums is therefore;

• Aave = (288 + 544) ÷ 2 = 416

Using integration, we have;

Distance INT(v(t)) = INT(2•t² + 8)) ≈ 405.3

Learn more about integration, here;

https://brainly.com/question/14330690