Moving object (differentiation)

[jgarcia]

Hello,

Having a challenge deciphering what this is asking me to do:

The position s(t) of an object moving along a straight line is given. Units of position are meters and times has units of seconds. In each case:

a) Find the objects velocity v(t) and acceleration a(t).

b) Find all times t when acceleration is 0 (zero).

s(t) = 2t⁴ – 5t³ + t – 3

so here is what I think it's asking:

I need to find the derivative to find the slope of its constant speed.

s'(t) = 2t⁴ – 5t³ + t – 3
s'(t) = 8t³ – 15t² + 1 – 0

and because v(t) = ds/dt ∴ v(t) = 8t³ – 15t² + 1

when t = 0

8(0)³ – 15(0)² + 1 = 1 or 1 m/s

then a(t) = dv/dt = d²s/dt² =

 

[stapel]

The position s(t) of an object moving along a straight line is given. Units of position are meters and times has units of seconds. In each case:

a) Find the objects velocity v(t) and acceleration a(t).
b) Find all times t when acceleration is 0 (zero).

s(t) = 2t⁴ – 5t³ + t – 3

so here is what I think it's asking:

I need to find the derivative to find the slope of its constant speed.

I'm not sure what you mean by "the slope of its constant speed", especially since the velocity function (being the first derivative of the position function) is not a constant function.

Instead, use what you've learned about the relationships between position, velocity, and acceleration. Given position function s(t), we have s'(t) = v(t) and s"(t) = v'(t) = a(t). Thus, for part (a), find the first and second derivatives. For part (b), set the second derivative equal to zero, and solve for the time(s) t.