questions about displacement, velocity and acceleration curves (1 Viewer)

[girlworld_club]

there is no actual explanation in textbooks. However there is always at least one question on this.

First of all if you are given a displacement curve:
where is acceleration zero?
where is velocity greatest?
where is velocity lowest?
when is acceleration greatest?

and if you are given an acceleration curve?
when is velocity constant?
when is velocity greatest?
where is the particle decellerating.


etc. etc. is there any easy way to understand this? or a logical method to use thanks soo much.

 

[Symphonicity]

are you using calculus?
the first derivative gives a function of velocity
and the second derivative gives a function of acceleration.

When f'(x) = 0, the particle is at rest. When f'(x) is >0, the curve is increasing. When it is <0, it is decreasing.
When f''(x) = 0, there is potentially a point of inflection which is where the concavity changes. When f''(x)>0, the curve is concave up and when it's <0, the curve is concave downwards.

If you are just analysing displacement/time graphs, a straight line graph where the line has a slope shows constant velocity. Velocity is greater the steeper the slope is. Acceleration is constant on this type of graph so you won't be able to say it's greatest or least at any point.

If you are looking at a velocity/time graph then a horizontal line shows constant velocity. A slope on the line shows acceleration. The steeper the slope, the greater the acceleration. So the steep slope will show a rapid increase in velocity but the greatest velocity will occur at the top of the graph, since the y axis is representing velocity. The particle is decelerating if the slope is negative, heading downhill. I hope that helps.