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.)

Question

f(t) = t^−1 − t

*We havent learned derivative yet but we have learned difference quotient and limits

Answer 1

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
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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

Answer 2

Damon, where did you get the -h from?

Answer 3

Damon, also how did you get f(t)=1/t -1? Shouldn't f(t)=1/t-t