Calculator Suite

Displacement Calculator

Calculate displacement, initial velocity, acceleration, or time using s = ut + ½at²

Displacement Problem Setup

Use s = ut + ½at² to solve for displacement, initial velocity, acceleration, or time

Object thrown upward - how far does it travel?

How far does an accelerating elevator travel?

How long to fall a certain distance?

Earth Gravity (-9.81 m/s²)

Displacement Formula

Second equation of motion for constant acceleration

s = ut + \frac{1}{2}at^2

$s$ = Displacement (change in position)

$u$ = Initial velocity

$t$ = Time

$a$ = Acceleration

Starting from average velocity and acceleration:

s = \bar{v} \cdot t = \frac{u + v}{2} \cdot t

Substituting v = u + at:

s = \frac{u + (u + at)}{2} \cdot t = ut + \frac{1}{2}at^2

Displacement vs Distance: Displacement is the change in position (vector), while distance is the total path length (scalar)

The ½at² Term: Represents the extra distance traveled due to acceleration

Sign Convention: Positive values indicate motion in the chosen positive direction

Projectile Motion: Calculating how far objects travel

Vehicle Analysis: Stopping distances and acceleration zones

Architecture: Elevator and escalator design

Sports: Track and field performance analysis

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