A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2+ 350. Include units in your answer.

What is the velocity of the ball after 2 seconds?

Question

A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2+ 350. Include units in your answer. 

What is the velocity of the ball after 2 seconds?

anonymous · Answer

$$velocity~ v=\frac{ ds }{ dt }=2 \times 4.9 t=9.8 t$$
plug t=2
and get the answer.

aryana_maria2323 · Answer

Is the answer 19.6?

aryana_maria2323 · Answer

@Aveline

aryana_maria2323 · Answer

Is that correct @anthonyym?

anthonyym · Answer

This is my guess on it:
The formula is already given: s(t) = 4.9t^2+ 350
Just plug 2 as t to get s(t), which is position.

You get 369.2 as s(t).

Velocity is distance/time. Distance is 369.2. Time is 2, so Velocity is 184.6

aryana_maria2323 · Answer

Yes but when you plug in that problem and solve for the derivative you get 9.8. so which way is correct?

anthonyym · Answer

Well I'm not in calculus, but my physics teacher told me that derivative is the slope. The slope of a position v. time graph is velocity and slope of velocity v. time is acceleration. Acceleration due to gravity is 9.8

aryana_maria2323 · Answer

Ohh okay. I will put both in my answer and I will let my teacher tell me which one is correct. Thank you.

anthonyym · Answer

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1000671.html Or check this example out, it says "velocity is the first derivative of displacement"

anthonyym · Answer

Yeah, my answer is probably wrong because the slope of the graph is not constant. You have to find the slope of the graph at t=3 with calculus probably which gets the velocity.

anonymous · Answer

19.6 is correct.