**TI 30Xa Algorithm: Acceleration, Velocity, Speed**

**Introduction
and Algorithm**

Given the acceleration (α), initial velocity (v0), and initial position (p0) of an object on a 2D plane, calculate velocity and position at time T.

Assuming that acceleration is constant, the equations are:

Acceleration: A = α

Velocity: V = α * t + v0

Position: P = α / 2 * t^2 + v0 * t + p0

With some simplification, we can simplify the work flow:

( I )

A = α

( II )

V = α * t + v0

V = A * t + v0 (II)

( III )

P = α / 2 * t^2 + v0 * t + p0

P = t * ( α / 2 * t + v0 ) + p0

P = t * ( α / 2 * t + 2 * v0 / 2 ) + p0

P = t * ( (α * t + 2 * v0) / 2 ) + p0

P = t / 2 * ( α * t + 2 * v0 ) + p0

P = t / 2 * ( α * t + v0 + v0 ) + p0

P = t * (V + v0) / 2 + p0

( I ): A = α

( II ): V = A * t + v0

( III ): P = t * (V + v0) / 2 + p0

Key Strokes:

1. Store the time T in Memory 1 ( T [ STO ] 1 )

2. Store the initial velocity in Memory 2 ( v0 [ STO ] 2 )

3. Enter the acceleration constant, α, press [ = ]

4. Calculate the velocity at time T: [ × ] [ RCL ] 1 [ + ] [ RCL ] 2 [ = ]

5. Calculate the position at time T: [ + ] [ RCL ] 2 [ = ] [ × ] [ RCL ] 1 [ ÷ ] 2 [ + ] p0 [ = ]

**Examples**

Example 1:

α = 1.3

v0 = 0

p0 = 0

T = 10

1. 10 [ STO ] 1

2. 0 [ STO ] 2

3. Acceleration: 1.3 [ = ]

4. Velocity: [ × ] [ RCL ] 1 [ + ] [ RCL ] 2 [ = ] (Result: 13)

5. Position: [ + ] [ RCL ] 2 [ = ] [ × ] [ RCL ] 1 [ ÷ ] 2 [ + ] 0 [ = ] (Result: 65)

Example 2:

α = -9.80665

v0 = 0

p0 = 10000

T = 30

1. 30 [ STO ] 1

2. 0 [ STO ] 2

3. Acceleration: 9.80665 [ +/- ] [ = ]

4. Velocity: [ × ] [ RCL ] 1 [ + ] [ RCL ] 2 [ = ] (Result: -294.1995)

5. Position: [ + ] [ RCL ] 2 [ = ] [ × ] [ RCL ] 1 [ ÷ ] 2 [ + ] 10000 [ = ] (Result: 5587.0075)

Example 3:

α = -0.05

v0 = 10

p0 = 20

T = 15

1. 15 [ STO ] 1

2. 10 [ STO ] 2

3. Acceleration: 0.05 [ +/- ] [ = ]

4. Velocity: [ × ] [ RCL ] 1 [ + ] [ RCL ] 2 [ = ] (Result: 9.25)

5. Position: [ + ] [ RCL ] 2 [ = ] [ × ] [ RCL ] 1 [ ÷ ] 2 [ + ] 20 [ = ] (Result: 164.375)

Example 4:

α = 4.26

v0 = 1.8

p0 = 0

T = 5

1. 5 [ STO ] 1

2. 1.8 [ STO ] 2

3. Acceleration: 4.26 [ = ]

4. Velocity: [ × ] [ RCL ] 1 [ + ] [ RCL ] 2 [ = ] (Result: 23.1)

5. Position: [ + ] [ RCL ] 2 [ = ] [ × ] [ RCL ] 1 [ ÷ ] 2 [ + ] 0 [ = ] (Result: 62.25)

Hope you find this useful.

**Happy
Halloween, Everyone!
**

Eddie

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