Asked by TayB
A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 5. (Round your answers to two decimal places.)
f(t) = t^−1 − t
*We havent learned derivative yet but we have learned difference quotient and limits
f(t) = t^−1 − t
*We havent learned derivative yet but we have learned difference quotient and limits
Answers
Answered by
Damon
If all in one direction, the velocity is the speed.
To get speed you need a speedometer.
To get velocity you need a speedometer and a compass.
If you knew derivatives this would be easy
v = df/dt = -1 (t^-2) - 1
= -1/t^2 - 1
for t = 5
v = -1/25 -25/25 = -26/25
--------------------------
if not then a mess as follows
f(t+h) = 1/(t+h) -t -h
f(t) = 1/t - t
f(t+h) - f(t) = 1/(t+h)- 1/t -h
= [ t -t - h ]/[t(t+h)] - h
divide by h
[ -1 ]/[t(t+h)] - 1
let h---> 0
-1/t^2 -1 like we said
To get speed you need a speedometer.
To get velocity you need a speedometer and a compass.
If you knew derivatives this would be easy
v = df/dt = -1 (t^-2) - 1
= -1/t^2 - 1
for t = 5
v = -1/25 -25/25 = -26/25
--------------------------
if not then a mess as follows
f(t+h) = 1/(t+h) -t -h
f(t) = 1/t - t
f(t+h) - f(t) = 1/(t+h)- 1/t -h
= [ t -t - h ]/[t(t+h)] - h
divide by h
[ -1 ]/[t(t+h)] - 1
let h---> 0
-1/t^2 -1 like we said
Answered by
TayB
Damon, where did you get the -h from?
Answered by
TayB
Damon, also how did you get f(t)=1/t -1? Shouldn't f(t)=1/t-t
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