Recall that: .slope = velocity.
. . . . . . .concavity = acceleration
Code:(1) | (2) | * | | | * | * |* * | * - * - - - * - - - * - - + - - -*- - - | * * | * | * * | | (3) | * (4) | | * * | * | * | * | * |* | * | | * - * - - - - - - - - + - - - - * - | |
Which graph has:
(a) Constant velocity
Constant velocity = constant slope.
If the slope doesn't change, we have a straight line . . . graph (4)
(b) Greatest initial velocity
The graph with the steepest slope at is graph (3).
(c) Greatest average velocity
Graph (1) has a slope that is positive sometimes, negative sometimes.
I suspect that the average velocity is 0.
Graph (4) has a constant negative slope.
Graph (3) always has a positive slope, but it is decreasing.
Graph (2) always has a positive slope and it is increasing.
I'd bet on Graph (2).
(d) Zero average velocity
As I suspected, it must be graph (1).
(e) Zero acceleration
Zero acceleration = zero concavity.
We must have a straight line . . . graph (4).
(f) Positive acceleration throughout
Positive accelration = positive concavity (concave up).
The curve that is always concave up is graph (2).