# Velocity and Acceleration--Derivatives

• Sep 23rd 2010, 09:21 PM
melliep
Velocity and Acceleration--Derivatives
Which graph has:

(a) Constant velocity

(b) Greatest initial velocity

(c) Greatest average velocity

(d) Zero average velocity

(e) Zero acceleration

(f) Positive acceleration throughout

Thank you =)
• Sep 23rd 2010, 10:15 PM
melliep
• Sep 23rd 2010, 10:17 PM
Soroban
Hello, melliep!

Recall that: .slope = velocity.
. . . . . . .concavity = acceleration

Quote:

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)

Quote:

(b) Greatest initial velocity

The graph with the steepest slope at $t = 0$ is graph (3).

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(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).

Quote:

(d) Zero average velocity

As I suspected, it must be graph (1).

Quote:

(e) Zero acceleration

Zero acceleration = zero concavity.

We must have a straight line . . . graph (4).

Quote:

(f) Positive acceleration throughout

Positive accelration = positive concavity (concave up).

The curve that is always concave up is graph (2).
• Sep 23rd 2010, 10:21 PM
melliep
you are utterly amazing. thank you so much i really really appreciate it.