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Acceleration vs. Velocity Equations

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Average Velocity

v a = (v 1 + v 0 ) / 2                    (1)

where

v a = average velocity (m/s)

v 0 = initial velocity (m/s)

v 1 = final velocity (m/s)

Final Velocity

v 1 = v 0 + a t                   (2)

where

a = acceleration (m/s 2 )

t = time taken (s)

Distance Traveled

s = (v 0 + v 1 ) t / 2                   (3)

where

s = distance traveled (m)

Alternative:

s = v 0 t + 1/2 a t 2 (3b)

Acceleration

a = (v 1 - v 0 ) / t                    (4)

Alternative:

a = (v 1 2 - v 0 2 ) / (2 s)                   (4b)

Example - Accelerating Motorcycle

A motorcycle starts with an initial velocity 0 km/h (0 m/s) and accelerates to 120 km/h (33.3 m/s) in 5 s .

The average velocity can be calculated with eq. (1) to

v a = ((33.3 m/s) - (0 m/s)) / 2

= 16.7 m/s

The distance traveled can be calculated with eq. (3) to

s = ( (0 m/s) + (33.3 m/s) ) (5 s) / 2

= 83.3 m

The acceleration can be calculated with eq. (4) to

a = ( (33.3 m/s) - (0 m/s) ) / (5 s)

= 6.7 m/s 2

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Related Topics

Dynamics

Motion - velocity and acceleration, forces and torque.

Related Documents

Acceleration

Change in velocity vs. time used.

Acceleration Units Converter

Converting between units of acceleration.

Average Velocity

Distance traveled vs. time used.

Car Acceleration

Car acceleration calculator.

Velocity Units - Online Converter

Convert between common velocity and speed units.

Velocity Units Converter

Convert between speed and velocity units like m/s, km/h, knots, mph and ft/s.

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