# Equations of motion Formula

Equations of motion or kinematic equations are the set of formulas describing the motion of a particle or the center of mass of a rigid body that is moving to a constant acceleration. They describe the behavior of the particle as it moves and as a function of time. The essence of all the equations is in the position of the particle, that is derived for the second law of Newton. From this all other motion characteristic can be derive.

position = initial position + (initial velocity)*time +1/2*(constant acceleration)*(time)^{2}

The equation is:

r = r_{0} + v_{0} t + ½ a t^{2}

Where:

r: position

r_{0}: initial position

v_{0}: initial velocity

a: acceleration

t: time

Equations of motion Formula Questions:

1) A particle is moving with a constant acceleration 2m/s^{2}, departing from position zero but with an initial speed of 10m/s, what is it position after 5 seconds?

Answer:

We replace the data the formula above:

r = 10m/s*5s + ½ 2 m/s^{2} * (5s)^{2}

r = 50 m + ½ 50 m = 75 m

2) Consider the same particle above, what is its velocity after those 5 seconds?

Answer:

The formula for the velocity is obtained deriving with respect to time the equation for the position.

V=d/dt (r_{0} + v_{0} t +1/2 a t^{2})=a*t

Then, the velocity is

V=2 m/s^{2} * 5 s = 10 m/s

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