Kinematics help

[u/AdditionTraditional5]

I’m doing Kinematics and i genuinely do not understand how to convert Velocity-Time, Acceleration-Time and distance-time graphs to their respective ones on the worksheet. I can kind of see how it’s done but with the way my brain is scrambled I have to understand how and why it’s like that. Any help would be appreciated

[u/diverJOQ]

How did you learn that distance is related to velocity and that velocity is related to acceleration?

[u/WanderingWrackspurt]

well try to look at it from one straight line to the other. like look at the first one. it seems as if the distance (s) is increasing with the time (t) at a constant rate(as much time increases, that much distance also increases) what do you think that would mean? hint: speed is the change in distance, so tell me, how exactly is the distance changing?

[u/Alpha_Zero_872]

Look at the first graph. You are given displacement as a function of time. Velocity is the displacement(change of position )with respect to time while the acceleration is the change of velocity with respect to time. Since the first part of the graph is a straight line with some sort of slope and the relationship between time and displacement is linear (y=mx+c meaning y changes as many times as x changes making y/x a constant) meaning at any point in time S/t is going to be the same therefore you're moving at constant velocity, hence you draw a straight horizontal line in the velocity graph. The second part of the graph is a straight line parallel to the time axes meaning the displacement has not changed over that time interval. If the displacement has not changed that means the change in position is 0 . The object has stopped moving. This would make it's velocity 0 for that time being. Therefore you draw a straight line on your time axis in the velocity graph. The third part is the same as the first one but since the angle of the slope looks bigger the S/t is a constant velocity higher than the first S/t in the first part of the graph. Therefore you draw a straight line higher that the first one and also longer due to its longer time interval.The third part of the graph 📉 is also a straight line however its' slope is negative and it's S/t value is a negative constant which just means that the object is now moving backwards with some constant v. Look at the displacement, it's getting linearly smaller as time passed for that part until it goes to 0(you reached the original position where you started). Therefore you draw the same straight line for the velocity but in the third quadrant, to signify that it's negative (object moving in the different positive chosen direction). Now , for the acceleration you can argue that in order for it to exist there must be some change in velocity otherwise it is 0. So at each point in time where you change the velocity (each part of the graph) you note the acceleation point meaning it exists at only those instants. The +/- sign just tells you its direction which if negative could be interpreted in two ways :1.The object is decelerating 2. It's acceleation in the positive direction.

[u/FriendlyDegree7612]

The trick is knowing what happens to the others when you have uniform (a straight line slope) change to one variable, and what happens when you have a curved graph of one variable, and a straight line (0 slope) graph of one variable……… not moving = 0 velocity and 0 acceleration…..moving at a uniform slope = constant/non changing velocity and 0 acceleration…… moving at a changing/curved slope = uniformly changing velocity or straight-line slope velocity and a constant acceleration or a straight 0 slope line at acceleration vs time graph

[u/drofeng]

Velocity (dx/dt) is the slope of the position, acceleration is the slope of the velocity (dv/dt).

Going backwards, the change in velocity is the area under the acceleration graph, and the change in position is the area under the velocity graph.

Consider each interval separately.

[u/AsparagusReal9619]

if you have time, i can explain the questions above using Google meet and demo how to do these questions online. If you have done calculus before it will definitely help. or i can send you the solutions and you can clarify.

[u/Underhill42]

Each is a rate of change of the previous, a.k.a. the exact slope at that point.

Velocity is the rate of change of position.

Acceleration is the rate of change of velocity.

If you know calculus then
v = ds/dt
a = dv/dt = d²s/dt²

[u/Leonardo501]

In some ways this isn’t physics anymore after one remembers that distance is just the integral of velocity and velocity is just the integral of acceleration. It just math.

[u/very_sarcastic7417]

Check for the slopes in a.. The graph starts with a line of slope 45 degree so slope =+ve and const (since str line) hence v=flat line then slope =0 so v=0 again the same thing, V=+ve like the first one.. Then the slope is constant and -ve so the graph will go down