Equations of Motion

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3.8Equations of Motion

In these revision notes for Equations of Motion, we cover the following key points:

  • Which equations are used in the uniform and non-uniformly accelerated (decelerated) motion?
  • How these equations transform when objects move vertically?
  • How does free fall differ from vertical motion?
  • How to apply the equations of motion in specific situations?

Equations of Motion Revision Notes

There are five basic equations of motion: one for the uniform motion and the other four, are for the uniformly accelerated (decelerated motion (motion with constant acceleration. For object moving horizontally, they are:

v = ∆x/∆t

for uniform motion and

v = v0 + a × ∆t
∆x = v + v0/2 × ∆t
v2 - v20 = 2 × a × ∆x
∆x = v0 × ∆t + a × ∆t2/2

for the uniformly accelerated (decelerated) motion.

When objects move vertically, displacement ∆x is replaced by the height h and the horizontal acceleration a is replaced by the vertical acceleration g, which is otherwise known as the "gravitational acceleration" (as it is caused by the gravity), or "acceleration of free fall." Therefore, the above equations become

Equation i

v = v0 + g × ∆t

Equation ii

h = v + v0/2 × ∆t

Equation iii

v2 - v20 = 2 × g × h

Equation iv

h = v0 × ∆t + g × ∆t2/2

If an object is released from a height, we say it is falling freely. There is no initial velocity involved in this kind of motion (which represents a special case of the uniformly accelerated or decelerated motion). Therefore, the four above equations become

Equation i

v = g × ∆t

Equation ii

h = v/2 × ∆t

Equation iii

v2 = 2 × g × h

Equation iv

h = g × ∆t2/2

When we are interested only in the scalar Kinematic quantities, we only replace ∆x with s, v with v, a with a, h with h, g with g without changing the structure of the abovementioned formulae.

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  5. Continuing learning kinematics - read our next physics tutorial: Position v's Time and Distance v's Time Graph

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