Velocity Calculator

Speed is a scalar quantity that measures how fast an object is moving (magnitude only). Velocity is a vector quantity that includes both speed and direction. An object traveling in a circle at constant speed has changing velocity because its direction changes. Average velocity considers displacement (straight-line distance from start to end), while average speed considers total distance traveled.

Use the formula v = d/t, where v is velocity, d is displacement (change in position), and t is time. For example, if a car travels 100 meters in 5 seconds, its velocity is 100/5 = 20 m/s. Remember that displacement is a vector, so velocity can be positive or negative depending on direction.

This equation calculates final velocity (v) when you know initial velocity (v0), constant acceleration (a), and time (t). For example, a car starting at 10 m/s and accelerating at 2 m/s2 for 5 seconds reaches v = 10 + (2)(5) = 20 m/s. This equation only works for constant (uniform) acceleration.

Use this equation when you need to find velocity but don't know the time. It relates final velocity (v), initial velocity (v0), acceleration (a), and displacement (d). For example, a ball dropped from 20m height (a = 9.8 m/s2, v0 = 0): v2 = 0 + 2(9.8)(20) = 392, so v = 19.8 m/s.

Common conversions: To convert m/s to km/h, multiply by 3.6. To convert m/s to mph, multiply by 2.237. To convert km/h to mph, multiply by 0.6214. For example: 30 m/s = 108 km/h = 67.1 mph. The speed of light is 299,792,458 m/s or about 1.08 billion km/h.

Average velocity is total displacement divided by total time. Instantaneous velocity is velocity at a specific moment, found using calculus (derivative of position) or by measuring over an infinitesimally small time interval. A car's speedometer shows instantaneous speed, while a trip average calculates average speed.

For a velocity v at angle theta from horizontal: the horizontal (x) component is vx = v*cos(theta) and vertical (y) component is vy = v*sin(theta). Conversely, from components: magnitude v = sqrt(vx2 + vy2) and angle theta = arctan(vy/vx). This is essential for projectile motion analysis.

Initial velocity (magnitude and angle), gravity (9.8 m/s2 downward), and air resistance. Without air resistance, horizontal velocity stays constant while vertical velocity changes due to gravity. Maximum range occurs at 45-degree launch angle. At the peak of trajectory, vertical velocity is zero but horizontal velocity continues.