finding distance

Good afternoon class, today we will be learning about how to measure distance traveled using left hand and right hand sums.

measuring distance when traveling at a constant velocity is relatively simple, just use the equation

Distance=Velocity x Time

For example, if Christine drove at 65 mph for 4 hrs., how far did she drive?
Distance= 65 mph x 4 hrs.
Distance =260 miles

It becomes slightly more difficult to measure distance when not travelling at a constant velocity, but it is simply a matter of a few extra steps.

For example, if Christine drove 80 mph for a 1/2 hr, 60 mph for 2 hrs, and 75 mph for an 3/2 hrs., how far did she drive?

Distance= (VxT) + (VxT) + ...

Distance = (80 x 1/2)+ (60 x 2) + (75 x 3/2)

Distance= 352.5 miles

another way to calculate distance would be to find the average of the left hand sum and the right hand sum.

T	0	2	4	6	8	10
MPH	60	62	65	68	69	70

 For example to calculate the left hand sum of the table above, you would find the distance the same way, but leave out the last two seconds.(T=10, mph= 70)

LHS= (60x2)+(62x2)+(65x2)+(68x2)+(69x2)

LHS= 648 miles

To calculate the right hand sum of the table above, you would use the same process as above, but instead of cutting out the last two seconds, you would cut out the first two.

RHS= (62x2)+(65x2)+(68x2)+(69x2)+(70x2)

RHS= 668 miles

calculating the average of the LHS and the RHS will give you a close estimate of the distance traveled. 

Average= (648+668)/2

Average=658 miles

That is how you find distance traveled using right hand and left hand sums, and tomorrow we will learn how to graph them.