Constant Acceleration Calculator

The constant acceleration calculator helps compute key motion parameters such as final velocity, displacement, acceleration, time, and average velocity for objects moving under uniform acceleration. It simplifies solving problems related to motion and is widely used in physics, engineering, and applied sciences.

Formula of Constant Acceleration Calculator

Step 1: Define the equations

The equations used for motion under constant acceleration are:

1. Final velocity:
   v = u + a * t
2. Displacement:
   s = u * t + (1/2) * a * t^2
3. Velocity-displacement relation:
   v^2 = u^2 + 2 * a * s
4. Average velocity:
   v_avg = (u + v) / 2

Where:
v is the final velocity in meters per second
u is the initial velocity in meters per second
a is the acceleration in meters per second squared
t is the time in seconds
s is the displacement in meters

Step 2: Solve for the desired variable

1. To calculate acceleration:
   a = (v – u) / t
2. To calculate time:
   t = (v – u) / a
3. To calculate initial velocity:
   u = v – a * t
4. To calculate displacement:
   s = (v^2 – u^2) / (2 * a)

Step 3: Choose the equation based on the available data

1. Use v = u + a * t if initial velocity, time, and acceleration are known.
2. Use s = u * t + (1/2) * a * t^2 if initial velocity, acceleration, and time are known.
3. Use v^2 = u^2 + 2 * a * s if initial velocity, final velocity, and acceleration are known.
4. Use v_avg = (u + v) / 2 to calculate average velocity or displacement.

Table of Common Calculations

Parameter	Formula	Example Value
Final velocity	v = u + a * t	25 m/s
Displacement	s = u * t + (1/2) * a * t^2	60 m
Time	t = (v – u) / a	5 s
Acceleration	a = (v – u) / t	4 m/s^2
Average velocity	v_avg = (u + v) / 2	12.5 m/s

Example of Constant Acceleration Calculator

Problem

A vehicle accelerates uniformly from rest (initial velocity = 0 m/s) with an acceleration of 3 m/s^2 for a duration of 10 seconds. Find its final velocity, displacement, and average velocity.

Solution

1. Calculate the final velocity:
   v = u + a * t
   v = 0 + (3 * 10) = 30 m/s
2. Calculate the displacement:
   s = u * t + (1/2) * a * t^2
   s = (0 * 10) + (1/2 * 3 * 10^2)
   s = 0 + 150 = 150 m
3. Calculate the average velocity:
   v_avg = (u + v) / 2
   v_avg = (0 + 30) / 2 = 15 m/s

Results

• Final velocity: 30 m/s
• Displacement: 150 m
• Average velocity: 15 m/s

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