Speed and Velocity Physics Notes
Speed and Velocity:
Speed: The speed of something is the rate at which it moves or travels. Speed is defined as the rate of movement of a body expressed either as the distance traveled divided by the time taken or the rate of change of position with respect to time at a particular point. It is a scalar quantity that refers to “how fast an object is moving.” “The time rate of distance is called speed.
Speed = \(\frac{\text { distance }}{\text { time }}\)
The unit of speed is m/s. The dimensional formula of speed is [M0LT-1]
Velocity: Velocity is the vector quantity that refers to “the rate at which an object changes its position.” Imagine a person moving rapidly one step forward and one step back-always returning to the original starting position. While this might result in a frenzy of activity. It would result in zero velocity. Because the person always returns to the original position.
The time rate of displacement is called velocity
velocity = displacement time
The following points may be noted about the speed of an object moving along a straight line:
- Speed is a scalar quantity. The magnitude of the velocity of the object is called its speed.
- The speed of an object in a particular direction is called the velocity of the object.
- The speed of an object has the same unit as that of velocity.
Types of Speed:
(a) Uniform speed: If a body covers equal distance in equal time intervals, howsoever small these intervals of time maybe is called uniform speed.
(b) Variable speed: If a body covers equal distances in unequal intervals of time or unequal distances in equal intervals of time, howsoever small these intervals of time maybe is called variable speed.
(c) Average speed: Average speed of a body is defined as the total distance travelled divided by the total time taken.
vav = \(\frac{\Delta x}{\Delta t}=\frac{x_{2}-x_{1}}{t_{2}-t_{1}}\)
(d) Instantaneous speed:
The speed of a body at any instant of time is called instantaneous speed. When we say about speed then it means about instantaneous speed. For this time interval should be very less or Δt → 0
The instantaneous speed of the vehicle is measured by the speedometer.
Types of velocity:
(a) Uniform velocity: It is defined as the ratio of the displacement to the time taken by the object to cover the displacement.
Uniform velocity = \(\frac{\text { displacement }}{\text { timeinterval }}\)
(b) Variable velocity: A body is said to be in variable velocity if it covers equal displacement in unequal intervals of time.
(c) Average velocity: Average velocity of a body is defined as the change in position or displacement (Δx) divided by time interval (Δt) in which that displacement occurs.
\(\overrightarrow{v_{a v}}=\frac{\Delta \vec{x}}{\Delta t}=\frac{\overrightarrow{x_{2}}-\overrightarrow{x_{1}}}{t_{2}-t_{1}}\)
(d) Instantaneous velocity: The instantaneous velocity of a body is the velocity of the body at any instant of time or at any point of its path.
\(\vec{v}=\frac{d \vec{x}}{d t}\)
Velocity can be positive, negative or zero.
By studying speed and velocity we come to the result that at any time interval average speed of an object is equal to or more than the average velocity but instantaneous speed is equal to instantaneous velocity.