The velocities for an accelerating car over a 4-second interval are given below:
t(s) | 0 0.5 1.0 1.5 2.0 2.5 3 3.5 4
-----
v(m/s) | 0 15 28 38 47 54 59 61 62
Estimate the distance traveled by the car during this time period by...
a) using the velocities at the beginning of the time intervals
b) using the velocities at the end of the time intervals

Question

kittybasil · Answer

This is a Calculus I problem! Redoing the table... t(s) | 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

v(m/s) | 0 15 28 38 47 54 59 61 62

Angle · Answer

a) left hand riemann sum
b) right hand riemann sum

kittybasil · Answer

So LHS, RHS and Midpoint basically differ only by the points with which the sub-interval rectangles are drawn?

kittybasil · Answer

well anyway idk how to Riemann it w/out a graph T_T

Zarkon · Answer

$$\sum_{i=1}^{n} v(t_{i}^{*})\Delta t$$

Zarkon · Answer

$\Delta t$= difference in consecutive times =.5

$t_i^*$=either

.5(i-1) or .5*i  (left or right)

Zarkon · Answer

for for the right

$$\sum_{i=1}^{n} v(t_{i}^{*})\Delta t=\sum_{i=1}^{8} v(.5i).5$$

$$=15*.5 +28  *.5 + 38 *.5 +  47*.5 +   54 *.5 +  59  *.5 + 61 *.5 + 62*.5$$

kittybasil · Answer

o_O

kittybasil · Answer

all this formal notation is killing my brain D:

Angle · Answer

kitty
you see that last line that zarkon wrote?
it was what I was talking about before
where the base of the rectangle is 0.5
and the rhs is made up of the v(m/s) points without the first 0

kittybasil · Answer

If I was required to write in $\Sigma$ notation I may mess things up. But I understand.

kittybasil · Answer

Thanks for your help everyone! @Zarkon @Angle