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Deportation Reckoner

Calculator Use

This Displacement Computer finds the distance traveled or deportation (southward) of an object using its initial velocity (u), dispatch (a), and time (t) traveled. The equation used is s = ut + ½at²; information technology is manipulated beneath to show how to solve for each individual variable. The figurer tin be used to solve for s, u, a or t.

Displacement Equations for these Calculations:

Deportation (s) of an object equals, velocity (u) times time (t), plus ½ times acceleration (a) times time squared (t^two).

\( s = ut + \dfrac{1}{2}at^2 \)

Where:
s = displacement
u = initial velocity
a = acceleration
t = time

Use standard gravity, a = 9.80665 chiliad/s², for equations involving the Earth's gravitational strength as the acceleration rate of an object.

Different resources utilise slightly unlike variables so yous might also run across this same equation with v_i or v₀ representing initial velocity (u) such as in the following form:

\( s = v_it + \dfrac{1}{2}at^ii \)

Where:
due south = displacement
v_i = initial velocity
a = acceleration
t = time

Displacement calculations used in calculator:

Solving for the different variables we can use the post-obit formulas:

Given u, t and a calculate due south
Given initial velocity, time and dispatch summate the displacement.
- s = ut + ½at²: solve for s
Given s, t and a calculate u
Given deportation, time and dispatch calculate the final velocity.
- u = s/t - ½at : solve for u
Given a, u and s calculate t
Given acceleration, initial velocity and displacement summate the fourth dimension.
- ½at² + ut - s = 0 : solve for t using the quadratic formula
Given s, t and u calculate a
Given displacement, fourth dimension and initial velocity calculate the dispatch.
- a = 2s/t² - 2u/t : solve for a

Displacement Problem 1:

A car traveling at 25 m/due south begins accelerating at 3 chiliad/s² for 4 seconds. How far does the car travel in the four seconds it is accelerating?

The 3 variables needed for distance are given as u (25 m/s), a (3 m/due southⁱⁱ), and t (4 sec).

southward = ut + ½at^two
s = 25 m/s * 4 sec + ½ * 3 m/s² * (four sec)² = 124 meters

Deportation Problem 2:

It takes a plane, with an initial speed of xx 1000/due south, 8 seconds to reach the end of the runway. If the plane accelerates at ten k/s², how long is the runway?

s = ut + ½at^two
s = 20 m/due south * viii sec + ½ * x 1000/s² * (viii sec)² = 600 meters