Graph descriptions of velocity, acceleration, speed and time

[asz304]

I can't understand the choices or the questions properly. And I want to know which of the following is right. I would appreciate it if you gave a hint or explanation. Thanks


1)For an object moving with constant positive acceleration, the displacement over a period of time could be found by taking:
a) integral of the velocity vs time graph.
b)integral of the acceleration vs time graph.
c)derivative of the velocity vs time graph.
d)derivative of the acceleration vs time graph.

2)For an object moving with constant positive velocity, the displacement vs time graph is:
a)parabolic with an intercept of zero.
b) linear with slope which is equal to the acceleration.
c)linear with slope which is equal to the velocity.
d)horizontal.

Sorry that I didn't add the template

 

[cepheid]

You can use simple dimensional arguments to figure out these questions. Imagine if the velocity were constant. Then the velocity-time graph would be flat, and the displacement would just be velocity*time, which would correspond to the area under the graph (a rectangle). You know this is right, because speed*time has units of length. The units have to work out. Now you're just considering a genaralization of that case to NON constant velocity (the graph is not flat anymore). The displacement is still given by the area under the curve, which still has the right units. It's just that a simple multiplication is no longer sufficient to calculate the area underneath a curve of arbitrary shape. You have to integrate.

 

[fss]

1)For an object moving with constant positive acceleration, the displacement over a period of time could be found by taking:

This is just a question about the relationship between acceleration, velocity, and displacement. If you know (or look up) how you go about finding one from another using basic calculus, you'll be able to get this quite easily.

2)For an object moving with constant positive velocity, the displacement vs time graph is:
a)parabolic with an intercept of zero.
b) linear with slope which is equal to the acceleration.
c)linear with slope which is equal to the velocity.
d)horizontal.

What does a graph of constant positive velocity look like? How do you get a displacement graph from a velocity graph?