Quick Answer

An object covering 100 meters in 10 seconds has a velocity of 10.00 m/s. An object starting from rest with acceleration 9.8 m/s squared for 5 seconds reaches 49.00 m/s.

Uniform Motion (v = d / t)

Solve For Velocity (v) Distance (d) Time (t)

Distance (m)

Time (s)

Accelerated Motion (v = v₀ + at)

Initial Velocity v₀ (m/s)

Acceleration (m/s²)

Time (s)

Common Examples

Input	Result
d = 100 m, t = 10 s	v = 10.00 m/s
d = 500 m, t = 25 s	v = 20.00 m/s
v0 = 0, a = 9.8 m/s^2, t = 5 s	v = 49.00 m/s
v0 = 15 m/s, a = 2.0 m/s^2, t = 10 s	v = 35.00 m/s
v = 30 m/s, t = 6 s	d = 180.00 m

How It Works

This calculator covers two standard velocity formulas from kinematics.

Uniform Motion

v = d / t

Where:

• v = velocity in meters per second (m/s)
• d = distance in meters (m)
• t = time in seconds (s)

This formula applies when an object moves at a constant speed in a straight line. The equation can be rearranged to solve for distance (d = v x t) or time (t = d / v).

Uniformly Accelerated Motion

v = v₀ + at

Where:

• v = final velocity (m/s)
• v₀ = initial velocity (m/s)
• a = acceleration (m/s^2)
• t = time (s)

This formula applies when an object experiences constant acceleration. It is one of the four standard kinematic equations. A positive acceleration increases velocity; a negative acceleration (deceleration) decreases it.

Velocity vs. Speed

Velocity is a vector quantity, meaning it has both magnitude and direction. Speed is the scalar magnitude of velocity. In one-dimensional problems, velocity can be positive or negative to indicate direction, while speed is always non-negative. This calculator works with the scalar component along one axis.

Common Velocity Values

• Walking speed: approximately 1.4 m/s (5 km/h)
• Running speed: approximately 3 to 8 m/s
• Speed of sound in air: approximately 343 m/s
• Speed of light in vacuum: approximately 3.0 x 10^8 m/s

Worked Example

A car travels 450 meters in 15 seconds at constant speed. Its velocity is v = 450 / 15 = 30.00 m/s (about 108 km/h). If the same car starts from rest (v₀ = 0) and accelerates at 3.0 m/s^2 for 10 seconds, its final velocity is v = 0 + 3.0 x 10 = 30.00 m/s. To find the time needed to accelerate from 20 m/s to 50 m/s at 5 m/s^2: t = (50 - 20) / 5 = 6.00 seconds.

Related Calculators

Acceleration Calculator

Calculate acceleration, velocity, or time using the kinematic formula a = (v2 - v1) / t.

Kinetic Energy Calculator

Calculate kinetic energy, mass, or velocity using the formula KE = ½mv².

Frequently Asked Questions

What is the difference between velocity and speed?

Velocity is a vector quantity that includes both magnitude and direction, while speed is a scalar that measures only magnitude. An object moving in a circle at constant speed has a changing velocity because its direction changes continuously. In straight-line (one-dimensional) motion, velocity and speed have the same magnitude but velocity can be negative to indicate reverse direction.

What units does this calculator use?

This calculator uses meters (m) for distance, seconds (s) for time, and meters per second (m/s) for velocity. To convert km/h to m/s, divide by 3.6. To convert mph to m/s, multiply by 0.44704. Acceleration is in meters per second squared (m/s^2).

When should I use the uniform motion formula vs. the accelerated formula?

The uniform motion formula v = d/t applies when speed is constant (no acceleration). The accelerated formula v = v0 + at applies when the object has a constant acceleration, meaning its velocity changes at a steady rate. If an object is speeding up or slowing down, the accelerated formula is appropriate.

Can velocity be negative?

Yes. A negative velocity indicates motion in the opposite direction of the positive reference axis. For example, if rightward is positive, then leftward motion has negative velocity. The formulas work correctly with negative values for velocity, acceleration, and even displacement.

What if acceleration is not constant?

The formula v = v0 + at assumes constant (uniform) acceleration. If acceleration varies over time, calculus-based methods (integration) are needed: v(t) = v0 + integral of a(t) dt. For many practical scenarios, using average acceleration provides a reasonable approximation.