The phase velocity of electromagnetic radiation may – under certain circumstances (for example anomalous dispersion) – exceed the speed of light in a vacuum, but this does not indicate any superluminal information or energy transfer. Otherwise, both the phase velocity and the group velocity vary with frequency, and the medium is called dispersive the relation ω = ω( k) is known as the dispersion relation of the medium. (That is: the envelope in such a situation changes shape so rapidly that group velocity loses its meaning.) Noting that c/ n = v p, indicates that the group speed is equal to the phase speed only when the refractive index is a constant d n/d k = 0, and in this case the phase speed and group speed are independent of frequency, ω/ k = d ω/d k = c/ n. Įxcept one cannot create a group with only a finite number of wave frequencies/wave vectors. The phase velocity is given in terms of the wavelength λ (lambda) and time period T as For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. This is the velocity at which the phase of any one frequency component of the wave travels. The phase velocity of a wave is the rate at which the wave propagates in any medium. The group velocity is positive, while the phase velocity is negative. The gradient of a displacement–time graph can have either a positive or a negative value, so it shows the direction of motion as well as the speed.This shows a wave with the group velocity and phase velocity going in different directions. using given equations to find velocities of objects dropped at rest.

It is represented by the gradient of a displacement–time graph. Some of the worksheets for this concept are Physics ap physics kinematics summer. Instantaneous velocity = rate of change of displacement. It is represented by the gradient of a distance–time graph. Instantaneous speed = rate of change of distance. Instantaneous values are defined in terms of the rate of change of distance or displacement and are represented by the gradients of the graphs. the average speed is constant for the first 10 s, after which it changes.Ĭalculations of the average speed or velocity over a period of time do not show any changes that have taken place.To calculate instantaneous velocity, the t needs to be zero. The equation for average velocity between the two points is: V x (t 2) x (t 1 )/ (t 2 -t 1) Let, t 1 t and t 2 t + t. over the 20 s time period, the average speed is 2 m s–1 and the average velocity is 0 X (t) is the position of x in respect to the function of t.The symbol c is usually reserved for the speed of light. When an object is changing speed/velocity, u is often used for the initial speed/velocity, with v being used for the final speed/velocity. The same symbols are used for speed and velocity. Information from the graphs can be used to calculate the average speed and average velocity over any time period, using the relationships:Īverage speed = distance travelled ÷ time taken v = Δd ÷ ΔtĪverage velocity = displacement ÷ time taken v = Δs ÷ Δt The fixed point is usually the starting point of the motion or the object’s rest position.

The diagram shows a distance–time graph and a displacement–time graph for the same motion.

displacement is a vector quantity it specifies both the distance and direction of an object measured from a fixed point.

As long as it is moving, the distance travelled by the object is increasing, but its displacement can increase or decrease and, like velocity, can have both positive and negative values. For an object moving along a straight line, positive (+) and negative (–) are usually used to indicate movement in opposite directions. Information about the speed of an object only states how fast it is moving the velocity also gives the direction.

Velocity formula physics