Acceleration Calculator
Calculate acceleration, final velocity, or time using the formula: a = Δv / t
Step-by-Step Solution:
1. Using the acceleration formula: a = Δv / t
2. Calculate the change in velocity:
Δv = v - v₀ = 20 - 0 = 20 m/s
3. Substitute the values:
a = 20 m/s / 5 s
4. Calculate:
a = 4 m/s per s
What is Acceleration?
Acceleration is the rate at which an object's velocity changes over time. When you speed up, slow down, or change direction, you are accelerating. It is one of the fundamental quantities in kinematics and dynamics.
Acceleration Formula:
a = Δv / t = (v − v₀) / t
where: - a = acceleration (measured in m/s²) - v = final velocity - v₀ = initial velocity - Δv = change in velocity (v − v₀) - t = time taken
This formula can be rearranged: - Final velocity: v = v₀ + a × t - Time: t = (v − v₀) / a
How to Calculate Acceleration
To find acceleration, follow these steps:
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Determine the initial velocity: How fast is the object moving at the start?
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Determine the final velocity: How fast is the object moving at the end?
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Measure the time interval: How long did the velocity change take?
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Calculate: Subtract initial from final velocity, then divide by time
Example: A car goes from 0 to 60 mph in 8 seconds. - a = (60 − 0) mph / 8 s = 7.5 mph/s
Positive vs. Negative Acceleration
Positive acceleration means the velocity is increasing in the positive direction — the object is speeding up.
Negative acceleration (deceleration) means the velocity is decreasing — the object is slowing down. When you apply the brakes in a car, the acceleration is negative.
Note: Acceleration can also be positive even when slowing down, if the object is moving in the negative direction. What matters is whether the acceleration and velocity point in the same direction (speeding up) or opposite directions (slowing down).
Uniform vs. Non-Uniform Acceleration
Uniform (constant) acceleration: The velocity changes at a steady rate. Free-falling objects near Earth's surface experience approximately uniform acceleration of 9.81 m/s².
Non-uniform acceleration: The rate of velocity change itself changes over time. Most real-world motion involves non-uniform acceleration (e.g., a car accelerating from a stop light).
Kinematic Equations
When acceleration is constant, several useful equations relate position, velocity, acceleration, and time:
- v = v₀ + at (final velocity)
- d = v₀t + ½at² (displacement)
- v² = v₀² + 2ad (velocity-displacement)
- d = ½(v₀ + v)t (average velocity)
These equations are the foundation of classical mechanics problem-solving.
Real-World Applications of Acceleration
- Automotive: Measuring 0-to-60 performance and braking distances
- Aviation: Calculating takeoff acceleration and g-forces on pilots
- Roller coasters: Designing safe but thrilling acceleration profiles
- Space exploration: Planning rocket trajectories and orbital maneuvers
- Sports: Analyzing sprinter acceleration off the blocks
- Seismology: Measuring ground acceleration during earthquakes
- Elevators: Designing smooth acceleration profiles for comfort
Common Questions About Acceleration
What is the formula for acceleration?
The acceleration formula is a = Δv / t = (v - v₀) / t, where a is acceleration, v is final velocity, v₀ is initial velocity, and t is time. It measures the rate of change of velocity.
What is acceleration?
Acceleration is the rate at which velocity changes over time. It is a vector quantity — it has both magnitude and direction. Positive acceleration means speeding up (in the positive direction), while negative acceleration (deceleration) means slowing down.
What is the SI unit of acceleration?
The SI unit of acceleration is meters per second squared (m/s²). This means the velocity changes by that many meters per second every second. For example, 3 m/s² means gaining 3 m/s of speed each second.
What is the acceleration due to gravity?
The acceleration due to gravity on Earth's surface is approximately 9.81 m/s² (or 32.17 ft/s²), often denoted as g. This means a freely falling object gains about 9.81 m/s of speed every second.
Can acceleration be negative?
Yes, negative acceleration (often called deceleration) means the object is slowing down relative to the positive direction. For example, a car braking from 30 m/s to 0 m/s has negative acceleration.