# Thread: [SOLVED] Best Graph Representation of s(t)

1. ## [SOLVED] Best Graph Representation of s(t)

Which graph best represents the position of a particle, s(t), as a function of time, if the particle's velocity and acceleration are both positive?

^^those are the possibilities for answers^^

For some reason, analytical problems like this always get me.

2. Velocity is the derivative of position. If the velocity is positive, the slope is positive. Here you should cross out D and E.

Acceleration is the derivative of velocity. If acceleration is positive, think of it as "the rate of change of the velocity is positive"...that is....the velocity is increasing. A doesn't show any increase in velocity. Cross it out.

The answer is C since it is increasing...it will not just reach a random limit and stop.

3. alternatively, note that velocity = s'(t) and acceleration = s''(t)

s'(t) > 0 means s(t) is an increasing function
s''(t) > 0 means s(t) is concave up

thus, C is the answer, it is the only increasing concave up function