How do you know what the Position vs. Time graph will look like?

Question

http://i18.tinypic.com/5yd2zgl.jpg
This is a v vs. t graph. How do you know what the position vs. time graph will look like?

Answer 1

ANSWER is B.

Mentally integrate V-t graph to get x.
Look at the t-x graph.
As time(t) goes forward x increases linearly, then flattens,
then decreases at a slower rate than the increase, which
is the B graph.

Answer 2

on the commencing up, that's merely no longer waiting to be complete precisely for this reason of actuality the fee/time graph aspects no indication of the quite area of the article. Mathematically (in case you will), this means that we've no longer any reference place to start up the graph. What we are waiting to do is come to a decision extra beneficial or much less how the situation is changing, so we are able to assume that the article starts at place 0. From 0 to a million 2d, the fee went from 0 to 2.5 m/s (i assume). we've no longer any counsel appropriate to the style of the fee curve in that era, so we are able to assume this is linear (meaning consistent acceleration). if so, the trouble-free velocity stands proud because of the fact the ordinary standard of the preliminary and very very final velocities: a million.25 m/s. With a recommend velocity of a million.25 m/s in a million 2d, the article will bypass a million.25 m. From a million 2d to 2 seconds, the fee would not substitute. With an analogous assumptions as above, the trouble-free velocity may be 2.5 m/s. in one 2d, the article will bypass 2.5 m. From 2d 2 to 2d 3, the assumed standard velocity is a million.875 m/s, so it strikes a million.875 m. You proceed in this way. Now, we are waiting to get our place/time counsel: first column seconds, 2d column meters. 0 0 - preliminary place a million a million.25 - preliminary place 0 + a million.25 meters moved 2 3.seventy 5 - preliminary place a million.25 + 2.5 meters moved 3 5.625 - preliminary place 3.seventy 5 + a million.875 meters moved And it is going on from there. be conscious that I particularly have paid no activity to significant digits - you will in all probability choose for to rectify that.

Answer 3

v(t) = x'(t)