Question

at time t, in seconds, your velocity, v, in ft/sec, is given by v(t) = 10 - t^2 for 0≤t≤3.
Use Δt = 1.5 to estimate total distance traveled during this time. find upper and lower estimates and then average the two

Answer 1

i am trying to put all of the pieces together but i am not really understanding for to use Δt

Answer 2

distance = rate * time
right
well velocity is your rate , delta t is the time
\[x(t) = v(t) * \Delta t\]
your intervals for t , are 0-1.5 and 1.5 -3
for upper use t = 1.5 , t=3
for lower use t = 0, t= 1.5

Answer 3

hmm okay one sec. figuring this out.

Answer 4

okay now I'm just having some trouble understanding what to plug in where

Answer 5

plug in t values into velocity function , delta t is just a constant (1.5)

Answer 6

lower:
\[v(0)*1.5 + v(1.5)*1.5\]

upper
\[v(1.5) *1.5 + v(3)*1.5\]

Answer 7

okay. what exactly does Δt mean?

Answer 8

length of time .... delta just means change
what this is saying is that for 1.5 sec the velocity stayed constant and the distance traveled is that velocity times time elapsed

Answer 9

okay. so now it asks me to sketch a graph of velocity vs time and show the left and right rectangles. does this mean i do this on the graph of v(t)=10 - t^2??

Answer 10

yes draw the parabola , then note the points on parabola where t = 0, 1.5, 3

Answer 11

thank you!!

Answer 12

yw
and as you will learn , the smaller your delta t , the more accurate the estimate