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Dynamics: Particle Acceleration

Acceleration is the change in velocity over time. Refer to equation 1.

Acceleration equation Straight Line (1)

dv = Change in velocity

dt = Change in time

If there is a constant acceleration that is being applied, equations 4 and 5 could be used to determine the velocity or displacement due to the constant acceleration. Equation 2 takes in consideration of an initial velocity, and equation 3 takes in consideration of an initial velocity and displacement.

Velocity equation Constant Acceleration (2)

vo = initial velocity

a c = constant acceleration

Velocity equation Constant Acceleration (3)

so = initial position

For example if a particle travelling at constant acceleration of 5 m/s2 with an initial velocity of 10 m/s after 5 seconds have past what would its new velocity and position be. The initial position can be set to 0.

v = 10 m/s + 5 m/s2 (5s) = 35 m/s

s = 0 + 10 m/s (5s) + 1/2 (5 m/s2) (5s)2 = 92.5 m

The above equations only consider an acceleration in one direction. However, we live in a 3-dimensional world which means that there coudl be an acceleration in the x-direction, y-direction, and z-direction. The magnitude of this acceleration can be determined by vector algebra as seen in equation 4.

Acceleration Magnitude (4)

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