Instantaneous Speed Homework - Caltech: Mechanical Universe

[AntonJD]

Homework Statement

I have just been watching Caltech: The Mechanical Universe and I'm a little bit puzzled by the instantaneous speed section, i understand the concept, if you try d/t you're deviding by zero at a fixed point so you can instead calculate ahead and reduce down to find the answer but the formula is what is puzzling me. The video shows V(t) = 2ct and elsewhere I'm being told it's v = vi + gt. Can someone shed some light on this or point me in the right direction.

Homework Equations

V(t) = 2ct
v = vi + gt

The Attempt at a Solution

N/A

 

[Doc Al]

The video shows V(t) = 2ct

What situation is that formula meant to describe?

and elsewhere I'm being told it's v = vi + gt.

That formula describes the vertical speed of a freely falling object, such as a ball tossed into the air. vi is the initial velocity; g is the acceleration due to gravity.

 

[AntonJD]

The formula was used to describe a roller coaster in free fall from a stopped position, and the formula was described as V(t) being velocity as a function of time, C as the distance which a body falls in the first second (which was given as 16ft or 5M). I've gotten myself so confused over this now that I've been trying to figure it out for about 2 hours, the most frustrating part is that I'm sure i understand the concept of it, just making sure i have the correct formula and expressing it as a formula is proving difficult.

 

[Doc Al]

The formula was used to describe a roller coaster in free fall from a stopped position, and the formula was described as V(t) being velocity as a function of time, C as the distance which a body falls in the first second (which was given as 16ft or 5M). I've gotten myself so confused over this now that I've been trying to figure it out for about 2 hours, the most frustrating part is that I'm sure i understand the concept of it, just making sure i have the correct formula and expressing it as a formula is proving difficult.

Perhaps the formula was V(t) = 2(c/t). That makes sense. c/t, which is distance traveled over time, gives the average velocity during that time. But the instantaneous velocity at the end of that time interval is twice that. (Note that it starts from rest.)