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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