Velocity Calculator
Calculate Velocity, Distance, Time & Acceleration Instantly
Calculate Velocity
What is Velocity?
Velocity is the rate at which an object changes its position. It is a vector quantity, meaning it has both magnitude (speed) and direction. Velocity tells us not only how fast something is moving but also in which direction it's moving. In physics, understanding velocity is fundamental to analyzing motion and predicting future positions of moving objects.
Key Characteristics of Velocity
- Vector Quantity: Has both magnitude and direction (unlike speed which is scalar)
- Can Be Negative: Negative velocity indicates motion in the opposite direction
- SI Unit: Meters per second (m/s), also km/h, mph, ft/s
- Average vs Instantaneous: Average velocity over time interval vs velocity at specific instant
- Constant or Changing: Constant velocity means no acceleration; changing velocity indicates acceleration
- Zero Velocity: Object at rest or returns to starting position
Speed vs Velocity
Understanding the distinction between speed and velocity is crucial:
Speed
- Scalar quantity (magnitude only)
- Always positive
- How fast you're moving
- Example: 60 km/h
Velocity
- Vector quantity (magnitude + direction)
- Can be positive or negative
- How fast and which direction
- Example: 60 km/h north
Velocity Formulas & Equations
Understanding the mathematical formulas for velocity is essential for solving physics problems. Here are the key equations you need to know.
Primary Velocity Formulas
Basic Velocity
Formula:
v = d / t
Where v is velocity, d is displacement (distance), and t is time
Final Velocity
Formula:
v = u + at
Where v is final velocity, u is initial velocity, a is acceleration, t is time
Velocity from Kinematic Equation
Formula:
v² = u² + 2as
Where s is displacement. Useful when time is unknown
Average Velocity
Formula:
v_avg = (v₁ + v₂) / 2
For constant acceleration. Also: v_avg = total displacement / total time
Detailed Example: Calculate Final Velocity
A car accelerates from 10 m/s at 2 m/s² for 5 seconds. Find the final velocity:
Given Information:
- Initial velocity (u) = 10 m/s
- Acceleration (a) = 2 m/s²
- Time (t) = 5 seconds
- Need to find: Final velocity (v)
Solution Steps:
Step 1: Use formula v = u + at
v = u + at
Step 2: Substitute values
v = 10 + (2 × 5)
Step 3: Calculate
v = 10 + 10 = 20 m/s
Result: The final velocity is 20 m/s. The car increased its speed by 10 m/s over the 5-second period due to the constant acceleration of 2 m/s².
Types of Velocity
Velocity can be classified into different types based on how it's measured and calculated. Understanding these distinctions is important for solving various physics problems.
Average Velocity
Formula: v_avg = Δd / Δt
Total displacement divided by total time. Gives overall velocity over a time interval, regardless of variations in between.
Instantaneous Velocity
Formula: v = lim(Δt→0) Δd/Δt = dd/dt
Velocity at a specific instant in time. Found using calculus (derivative of position). Shows velocity at exact moment.
Constant Velocity
Characteristic: No acceleration (a = 0)
Object moves at same speed and direction. Displacement equals velocity times time: d = vt. No change in velocity over time.
Variable Velocity
Characteristic: Acceleration present (a ≠ 0)
Velocity changes over time due to acceleration. Requires kinematic equations: v = u + at. Most real-world motion involves variable velocity.
Velocity Unit Conversions
Velocity can be measured in various units depending on the context. Here are common units and their conversion factors.
Common Velocity Units
Frequently Asked Questions
Disclaimer: This velocity calculator provides accurate results based on standard physics formulas: v = d/t, v = u + at, and v² = u² + 2as. Calculations assume ideal conditions without air resistance or friction unless otherwise specified. For educational and general physics calculations. Always verify critical results independently and consider real-world factors for practical applications. SI units (m/s) are standard; conversions to other units are approximations.