Question

Can someone please verify my answer?
At time t minutes, an object's distance from a point is given by s(t) feet.
Which of the following represents the instantaneous rate of change of the velocity of the object at time t?

Answer 1

http://www.1728.org/velocity.htm
I find this website very helpful you should give it a try

Answer 2

The choices:
\[s''(t)\]
\[\lim_{h \rightarrow 0} \frac{ s''(t+h) - s''(t) }{ h }\]
\[\lim_{h \rightarrow 0}\frac{ s(t+h) - s(t) }{ h }\]
\[\frac{ s'(t+h) - s'(t) }{ h }\]
\[\frac{ s'(t+1) - s'(t) }{ 1 }\]

Answer 3

At first I thought it was the second limit, but that proved to be wrong.

Answer 4

Based on your website I'm thinking it is the first limit I wrote as an option.

Answer 5

The instantaneous rate of change of velocity = \(\bf v'(t)=a(t)\). So basically it's the derivative of velocity. We know that velocity is the derivative of position hence: \(\bf v'(t)=a(t)=s''(t)\)

Answer 6

@iamsammybear

Answer 7

Thank you so much! So it would be the first limit I wrote above.

Answer 8

\(\bf a(t)=acceleration \ with \ respect \ to \ time\)

Answer 9

It would be the first choice, yes.