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 = 3.
f(t) = (t ^-1) - t

Question

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 = 3. 
f(t) = (t ^-1) - t

anonymous · Answer

i think the inverse of the t is kicking me

bahrom7893 · Answer

V(t)=S'(t) = -1*t^(-2) - 1.
When t = 3
V(t) =[  - 1 / (3^2) ] - 1
V(t) = -1/9  -  1
V(t) = -10/9

mathteacher1729 · Answer

Position = f(t) 
Velocity = f'(t) [ 1st derivative of position]
Acceleration = f''(t) [2nd derivative of position, or 1st derivative of velocity]

We can write the position function like this, if it helps.

$$f(t) = t^{-1}-t = \frac{1}{t}-t$$

bahrom7893 · Answer

Speed is the same as velocity but it doesn't have direction, so you just need the absolute value of velocity
Speed = | V(t) | = | - 10/9 | = 10/9