Constant Acceleration Equations Calculator

Science - Physics - Formulas

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Problem:

Solve for velocity.

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Solution:

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	velocity
	acceleration
	time
	initial velocity

	average velocity
	initial velocity
	velocity

	distance or displacement
	time
	average velocity

v	=	final or end velocity
v0	=	initial velocity
a	=	acceleration
t	=	time
vave	=	average velocity
Δx	=	distance displacement

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References - Books:

Tipler, Paul A. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.

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Background

When an object moves in a straight line with an initial velocity and is subjected to constant acceleration, the principles of kinematics can be used to determine the object's velocity at any given time. Kinematics is the study of motion without considering the forces causing the motion. The velocity of an object is a measure of how fast it is moving in a particular direction, and acceleration is the rate of change of velocity. Understanding how to calculate the velocity of an object, given its initial velocity and constant acceleration, is fundamental in physics and various applied fields.

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Equation

The equation to calculate the final velocity (v) of an object given its initial velocity (v₀) and constant acceleration (a) over a time period (t) is:

v = v₀ + at

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How to Solve

To solve for the final velocity using the above equation, follow these steps:

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Example

Consider a car accelerating from rest (v₀ = 0 m/s) with a constant acceleration of 3 m/s^2 for a duration of 5 seconds.

Using the equation:

v = v₀ + at

Substitute the given values:

v = 0 m/s + 3 m/s² x 5 s

Calculate:

v = 15 m/s

Hence, the car's final velocity after 5 seconds is 15 m/s.

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