Interpreting Distance vs Time graphs to Velocity and Acceleration?

Question

Hi, I'm going into AP physics this year, and I know this may sound like a beginner question to some...but I have to know for sure.

When I first learned D vs T graphs and then learned to draw them into V vs T and then A vs T, I was using straight slopes. However, AP physics presents the lines as curved. If the D vs T graph has curves in it, will the V vs T and A vs T graphs have curves in them as well?

Answer 1

Yes

Answer 2

It depends.
If the D vs T graph is exponentially curving (or gaining a steeper and steeper slope) that means it represents constant acceleration, therefore, the A vs T graph won't curve (straight horizontal line), also the velocity is increasing constantly so the V vs T graph won't curve (straight diagonal line).

If the D vs T graph has any other type of curve than both the V vs T and the A vs T graph will have curves.

Answer 3

It relies upon. If the D vs T graph is exponentially curving (or gaining a steeper and steeper slope) meaning it represents consistent acceleration, for this reason, the A vs T graph won't curve (rapidly horizontal line), additionally the fee is increasing continuously so the V vs T graph won't curve (rapidly diagonal line). If the D vs T graph has the different form of curve than the two the V vs T and the A vs T graph might have curves.

Answer 4

Actually, a constant acceleration can produce a linear velocity graph and a parabolic position graph. If you move from position to velocity to acceleration, you have the degree of the equation going down by one each time, so the curve straightens, if you see what I mean.

This will all make more sense once you have some calculus to do physics with.

Answer 5

Maybe yes, maybe no. In terms of equations

if d = t^2 ( a curve) then v = 2t ( straight) and a = 2 ( straight constant)

but if d = t^3 ( a curve) then v = 3t^2 ( curved) and a = 6t ( straight)

Keep going with d = t^4 and a will be curved also.....

Answer 6

The reason it will curve is because the object is accelerating.
v=d/t in a linear graph right? thats when you get constant velocitie. or v
In the case of accelaration
it is also a simple formulae a=d/t^2 because your velocitie is accelerating your segonds are square
t*t or t^2
Use the a=d/t^2 and you'll see, your line will curve.