Thread: [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?

http://www.utexas.edu/academic/mec/gif/p5.gif

^^those are the possibilities for answers^^

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

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.

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