Acceleration in Feet per Second Squared Calculator
Calculate and convert acceleration in physics with an easy-to-use tool
Perfect for engineers, students, and physics enthusiasts
Acceleration Calculator (ft/s²)
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Acceleration Visualization
Understanding Acceleration in Feet per Second Squared
What is Acceleration?
Acceleration is the rate at which the velocity of an object changes over time. In physics, it is a vector quantity that has both magnitude and direction. When an object speeds up, slows down, or changes direction, it is accelerating.
The unit “feet per second squared” (ft/s²) represents how much the velocity changes, measured in feet per second, during each second of time. For example, an acceleration of 5 ft/s² means that the object’s velocity increases by 5 feet per second every second.
Acceleration Formulas
Using Velocity Change:
a = acceleration (ft/s²)
vf = final velocity (ft/s)
vi = initial velocity (ft/s)
t = time (seconds)
Using Distance & Time:
a = acceleration (ft/s²)
d = distance traveled (ft)
vi = initial velocity (ft/s)
t = time (seconds)
Using Force & Mass:
a = acceleration (ft/s²)
F = force (pounds-force)
m = mass (slugs)
Common Acceleration Values
| Scenario | Acceleration (ft/s²) | Comparison to g |
|---|---|---|
| Gravity at Earth’s surface | 32.17 | 1.00g |
| Typical car acceleration (0-60 mph in 8 sec) | 11.00 | 0.34g |
| Sports car acceleration (0-60 mph in 3 sec) | 29.33 | 0.91g |
| Emergency braking in a car | 28.00 | 0.87g |
| Roller coaster (typical maximum) | 48.26 | 1.50g |
| Space shuttle during launch | 96.52 | 3.00g |
| Fighter jet maneuvers | 289.57 | 9.00g |
Acceleration Unit Conversion Tables
Feet per Second Squared to Other Units
| Feet per Second² (ft/s²) | Meters per Second² (m/s²) | G-force (g) | Miles per Hour per Second | Inches per Second² (in/s²) |
|---|---|---|---|---|
| 1 | 0.3048 | 0.03108 | 0.6818 | 12 |
| 5 | 1.524 | 0.1554 | 3.409 | 60 |
| 10 | 3.048 | 0.3108 | 6.818 | 120 |
| 20 | 6.096 | 0.6217 | 13.636 | 240 |
| 32.174 (standard gravity) | 9.807 | 1.000 | 21.937 | 386.088 |
| 50 | 15.24 | 1.554 | 34.091 | 600 |
| 100 | 30.48 | 3.108 | 68.182 | 1200 |
Other Units to Feet per Second Squared
| Unit | Value | Feet per Second² (ft/s²) |
|---|---|---|
| Meters per Second² (m/s²) | 1 | 3.281 |
| G-force (g) | 1 | 32.174 |
| Miles per Hour per Second | 1 | 1.467 |
| Inches per Second² (in/s²) | 12 | 1 |
| Centimeters per Second² (cm/s²) | 100 | 3.281 |
| Kilometers per Hour per Second (km/h/s) | 1 | 0.9113 |
Practical Examples of Acceleration Calculations
Example 1: Car Acceleration
Problem: A car accelerates from 0 to 60 mph in 8 seconds. What is its acceleration in feet per second squared?
- Convert the velocities to feet per second:
- Initial velocity: 0 mph = 0 ft/s
- Final velocity: 60 mph = 60 × 1.467 = 88.02 ft/s
- Use the acceleration formula: a = (vf – vi) / t
- Substitute the values: a = (88.02 – 0) / 8 = 11.00 ft/s²
Answer: The car’s acceleration is 11.00 ft/s², which is approximately 0.34g (about one-third of gravity’s acceleration).
Example 2: Falling Object
Problem: A rock is dropped from a cliff. How far will it fall in 3 seconds, assuming it starts from rest?
- We know that objects on Earth accelerate due to gravity at approximately 32.17 ft/s²
- Initial velocity (vi) = 0 ft/s (since it starts from rest)
- Time (t) = 3 seconds
- Use the formula: d = vit + ½at²
- Substitute the values: d = 0 × 3 + ½ × 32.17 × 3² = 144.77 feet
Answer: The rock will fall approximately 144.77 feet in 3 seconds.
Example 3: Rocket Launch
Problem: A model rocket with a mass of 0.5 slugs is propelled upward by a force of 20 pounds. What is its initial acceleration?
- We need to account for both the propulsion force and the force of gravity
- Propulsion force = 20 lbf upward
- Gravity force = mass × g = 0.5 slugs × 32.17 ft/s² = 16.09 lbf downward
- Net force = 20 – 16.09 = 3.91 lbf upward
- Use Newton’s Second Law: a = F/m
- Substitute the values: a = 3.91 / 0.5 = 7.82 ft/s²
Answer: The rocket’s initial acceleration is 7.82 ft/s² upward.
Frequently Asked Questions
Speed is the rate at which an object covers distance (how fast it’s moving), typically measured in feet per second, miles per hour, or meters per second. It’s a scalar quantity that only considers magnitude.
Acceleration is the rate at which speed changes over time, measured in units like feet per second squared (ft/s²). It’s a vector quantity with both magnitude and direction. When you press your car’s gas pedal, you’re causing it to accelerate—to change its speed.
Negative acceleration, also called deceleration, means that an object is slowing down. The negative sign indicates that the acceleration is in the opposite direction of the velocity.
For example, when you apply the brakes in a car, you’re creating a negative acceleration that reduces your speed. If a car is traveling at 88 ft/s (60 mph) and comes to a stop in 4 seconds, its acceleration is -22 ft/s² (negative because the speed is decreasing).
Acceleration is central to Newton’s Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Mathematically, this is expressed as F = ma (Force = mass × acceleration), or when solving for acceleration, a = F/m. This means:
- More force on an object results in greater acceleration
- More massive objects require more force to achieve the same acceleration
Acceleration is measured in units like “feet per second squared” (ft/s²) because it represents the change in velocity (which is already measured in feet per second) over time (in seconds).
When we divide a velocity unit (ft/s) by time (s), we get ft/s² as the unit for acceleration. This tells us how many feet per second the velocity changes each second.
For example, an acceleration of 5 ft/s² means that every second, the object’s velocity increases by 5 feet per second. After 1 second, it’s moving 5 ft/s faster than initially; after 2 seconds, it’s moving 10 ft/s faster, and so on.
The standard acceleration due to gravity on Earth’s surface is approximately 32.17405 feet per second squared (ft/s²), or 9.80665 meters per second squared (m/s²). This value is commonly denoted as ‘g’.
This means that an object falling freely near Earth’s surface will increase its velocity by about 32.17 feet per second every second it falls (ignoring air resistance).
The value of gravitational acceleration varies slightly across Earth’s surface due to factors like latitude, altitude, and local geological variations, but 32.17 ft/s² is used as the standard value for calculations.
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