The following table gives the velocity v(t) (in feet per sec) at different instances of time t (in sec) of a particle moving along a horizontal axis.

t 0 4 8 12 16 20
v(t) 43 42 40 35 25 5

Estimate the distance traveled by the particle between t = 0 sec and t = 20 sec using 5 time intervals of equal length with

(a) left endpoints
Estimated distance = _____feet

(b) right endpoints
Estimated distance = _____feet

1. 👍 0
2. 👎 0
3. 👁 282
1. t 0 4 8 12 16 20

vt 43 42 40 35 25 5

1. 👍 0
2. 👎 0
2. left endpoints: 4*43 + 4*42 + ... + 4*25
right ends: 4*42 + 4*40 + ... + 4*5

1. 👍 0
2. 👎 0
3. hey thanks but i still don't get how you arrived to this answer?

1. 👍 0
2. 👎 0
4. consult your text, or do a web search. To approximate the area under a curve, draw rectangles of (in this case) width 4.

The vertical sides intersect the curve at various points. To approximate using left endpoints, make the height of the rectangle spanning x0-x1 the value of f(x0) - the left height.

Thus, the area of rectangle from xi to xi+1 is w*f(xi)

Using the right endpoints of the intervals, the area is w*f(xi+1)

Takes a lot of words, but any illustration should make it clear.

Why are we approximating the area under the curve? Because we are given the speed at various times. speed is the derivative of the position. The position is thus the integral of the speed over an interval.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### algebra. help!

Start from 110 feet away, a person on a bicycle rides towards a checkpoint and then passes it. The rider is travelling at a constant rate of 30 feet per second. The distance between the bicycle and the checkpoint is given by the

2. ### Calculus

A 15 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time t=0 and slides away from the wall at a rate of 3ft/sec. Find the velocity of the top of the ladder at time t=2. The velocity of ladder at

3. ### Math

Starting from 130 feet away, a person on a bicycle rides towards a checkpoint and then passes it. The rider is traveling as a constant rate of 25 feet per second. The distance between the bicycle and the checkpoint is given by the

4. ### Bubbles

starting from 105 feet away a person on a bicycle rides towards a checkpoint and then passes it. the rider is traveling at a constant rate of 35 feet per second. THe distance between the bicycle and the checkpoint is given by the

1. ### Math

For this problem, a person standing on the edge of a cliff throws a rock directly upward. it is observed that 2 secs later the rock is at its maximum height (in feet) and that 5 secs after that (meaning 7 seconds after being

2. ### College Algebra

Use the position equation given below, where s represents the height of the object (in feet), v0 represents the initial velocity of the object (in feet per second), s0 represents the initial height of the object (in feet), and t

3. ### calculus

The table below gives the height h=f(t) in feet of a weight on a spring where t is time in seconds. t (sec) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 h (feet) 4.8 7 8 8.3 8 7 4.8 2.6 1.6 1.3 1.6 2.6 4.8 7 8 8.3 (a) What is the

4. ### Quick calc question

Find the distance, in feet, a particle travels in its first 2 seconds of travel, if it moves according to the velocity equation v(t)= 6t2 − 18t + 12 (in feet/sec). 4 5

1. ### Calculus

A girls throws a tennis ball straight into the air with a velocity of 64 feet/sec. If acceleration due to gravity is -32 ft/sec2, how many seconds after it leaves the girl's hand will it take the ball to reach its highest point?

2. ### Science

Four students each added salt crystals to water and measured the time it took for all the crystals to disolve. The following table shows their results. A three-column table, with column headers 'Student, 'Temperature (°C), 'and

3. ### Math

Using h(t)=gt^2+v0t+h0, where g= -16, h0= initial height, v0= initial velocity, and t= time A rocket is fired into the air from the top of a building that is 200 feet tall. The initial velocity of the rocket is 600 feet/sec. If

4. ### physics

A rolling ball moves from x1 = 3.2 cm to x2 = -4.4 cm during the time from t1 = 3.4 sec to t2 = 6.2 sec. What is its average velocity?