# Velocity

# Velocity

Velocity, in physics, is defined as the time rate of change of the position of a body. Mathematically, velocity is a vector quantity having direction as well as magnitude (length). Speed, on the other hand, is a scalar quantity that has only magnitude. An object moving with constant velocity (v) during a particular period (t) along a straight line has a certain displacement (s). This motion is described with the equation: v = s/t.

For example, an automobile runs at a constant rate for two hours and travels north for 120 miles on a straight stretch of road. Its velocity contains both a directional and a magnitude component. Its direction is north and its magnitude (speed) is v = s/t = 120 miles/2 hours = 60 miles per hour. As seen, the magnitude of velocity is expressed in units such as miles per hour or meters per second when describing motion along a straight or curved path. The International System of Units (SI) for velocity is meters per second.

A body sometimes does not maintain constant speed during a trip. When this happens, an average velocity can be calculated. One of the simplest ways to calculate average velocity (v_{av}) is to add the initial velocity (v_{initial}) and the final velocity vfinal and divide by two; that is, v_{av} = (vinitial + vfinal)/2.

For example, an automobile that travels at v_{initial} = 55 miles per hour for the first half of a trip but then speeds up to v_{final} = 65 miles per hour for the last half of the trip, would have an average velocity of (55 miles per hour + 65 miles per hour)/2 = 60 miles per hour (that is, assuming the automobile is traveling in the same direction for the entire time, so that its directional component remains the same).

A body that is rotating about an axis has angular velocity. Angular velocity is also a vector quantity and is expressed as units of angular rotation (w) per unit of time (t) such as revolutions per minute or radians per second.

For example, if a rider on a carousel goes around once every 30 seconds, then the rider makes one 360° revolution every 30 seconds. Thus, v = w/t = 360°/30 seconds = 12%deg; per second. The SI unit for angular velocity is radians per second (where 360° equals 2π), but other units are also commonly used such as revolutions per minute (rpm).

# velocity

**velocity (symbol v)** Rate of motion of a body in a certain direction. Velocity is a vector (magnitude and direction), whereas speed, which does not specify direction, is a scalar. Velocity can also be a measurement of how quickly an object changes its position in a given direction. An object's velocity can be found in the same manner as speed, by dividing the distance

*s*it has travelled by the time

*t*taken, and this is expressed as

*v=s/t*and given in metres per second (ms

^{-1}) or kilometres/miles per hour. Velocity is then stated, for example, as ‘60kph/37mph eastward’. Positive and negative values to represent movement in opposite directions can be shown on both a velocity-time graph and a displacement-time graph (movement from a fixed position).

# velocity

ve·loc·i·ty / vəˈläsətē/ • n. (pl. -ties) the speed of something in a given direction: *the velocities of the emitted particles.* ∎ (in general use) speed: *the tank shot backward at an incredible velocity.* ∎ (also ve·loc·i·ty of cir·cu·la·tion) Econ. the rate at which money changes hands within an economy.

# Velocity

# Velocity

Velocity is the time **rate** of change of the position of a body. Mathematically, velocity is a vector quantity having direction as well as magnitude. Speed, on the other hand, is a **scalar** quantity which has only magnitude. The magnitude of velocity is expressed in units such as miles per hour or meters per second when describing **motion** along a straight or curved path. A body which is rotating about an axis has angular velocity. Angular velocity is also a vector quantity and is expressed as units of angular **rotation** per unit of time such as revolutions per minute or radians per second.

# velocity

**velocity** swiftness of motion XVI; rapidity of operation XVII. — (O)F. *vélocité* or L. *vēlōcitās*, f. *vēlox* swift, rapid; see -ITY.

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