Time rate of change of distance is called speed. Speed defines “How fast an object is moving?”. Speed is a scalar quantity. It has magnitude only. Speed is not defined by direction of the motion. Dimension of speed is [LT-1].
Consider a body is moving along a path ‘L’. It covers a distance 'S' in time interval 't’. Then the speed ‘R' of the moving object is given by the formula
R = S / t
Ris the speed
Sis the distance travelled
tis the time taken to travel distance S.
SI unit of speed is metre per second (
ms-1), most commonly used to measure the speed of animals, humans and free-falling objects . Other units are kilometre per hour (written in abbreviated version as
kmh-1) and miles per hour (symbol is
mph-1). These are derived units of speed. Speedometers of vehicles mostly use
kmh-1 to show the speed. Another unit of speed is knots, used in measuring the speed of boats and ships.
We can convert one unit of speed to other by multiplying with a suitable conversation factor. For example, if we want to convert
18ms-1 into kilometre per hour, suitable factor to multiply will be
18 × 3600 = 64,800 mh-1
64,800 ÷ 1000 = 648 kmh-1
Ratio of the total distance to the time taken to travel the total distance is called average speed. It is an estimated rate at which the motion takes place. Formula of average speed is
Average speed = total distance travelled / total time taken
speed of a body at a particular instant of time, when ∆t following the time t approaches to zero. Formula of instantaneous speed is
Instantaneous speed = limit as ∆t approaches to zero ( ∆S/∆t).
Time rate of change of displacement is called velocity. Velocity is a vector quantity. It is defined completely by magnitude and direction. Dimension of velocity is
[ LT -2 ]
speed is also known as magnitude of velocity. Direction itself does not has any unit. So velocity and speed have unit in common. Velocity is represented by small bold v (v). Formula to calculate velocity is
Velocity v = displacement d / Time t
Use our velocity calculator to measure velocity. It is completely functional and easy to use. Enter distance and time in meters and seconds respectively and calculate velocity easily.
As formula for speed and velocity are same, units of velocity and speed are also same.
Consider a body travel a distance d in time t then average velocity of the body is given by formula
Vav = d / t
- Vav is average velocity
- d is displacement
- t is time.
One cannot tell about the motion between two points using average velocity. For example, if a squash ball is hit on a wall, it comes back after striking the wall. Initial and final position are same, so average velocity is zero. But we know that ball has covered some distance. Hence, average velocity cannot tell about the motion. This problem is sorted out using instantaneous velocity.
Concept of instantaneous velocity can be understood with the help of following example. Let a body be moving along path DFG in Cartesian plan. At any instant t, the body is at point
D. Position of body is represented by
r1 (position vector). Let the body be at point
F, after a small interval of time
(∆t) following the time
t. This position of body is represented by
r2. Displacement of the body in travelling from
∆d = r2 – r1
∆ means a small change.
If we bring F close to D by making
∆t smaller and smaller,
∆d will also become smaller relatively and a point a will reach when
∆t will become almost zero but will not completely disappear. Velocity at this particular instant is called instantaneous velocity.
Instantaneous velocity is expressed in mathematical form as
Vins = limit as ∆t approaches to zero (∆d/∆t)
If the instantaneous velocity remains constant, velocity of body remains constant.
When a body is moving along a straight path, the velocity of the body is linear.
when a body is moving in a circle, it’s moving with angular velocity and it is directed towards the centre of the circle.
Real life examples:
we use the concept of velocity in daily life a lot. Following are some examples.
- When one is driving a car from office back to home. There must be some speed (magnitude of velocity) with which the car is being driven and of course a direction also. Let the car be moving with
140kmh-1in south. Speed and velocity both are
140kmh-1. Now if you reverse your car after stopping for a while at a speed of
20kmh-1. You velocity will be
- Minute hand of a watch moves with a velocity of 0.0017
- Satellites are set into an orbit around the earth while keeping in view ‘escape velocity'
- A ball thrown upward goes up with a decreasing velocity while comes back with increasing velocity. Average velocity is zero.
- In the world of cricket, a Bowler always has a bowling speed or velocity with which it bowls the ball. For example, bowling speed of Wahab Riaz, a Pakistani bowler, is
If the velocity of the body does not remains constant, body is said to possess acceleration. Time rate of change of velocity is called acceleration.
Acceleration is also a vector quantity. Acceleration may be produced by a change, whether in magnitude or direction of velocity. Dimension of acceleration is
[LT-2]. It is represented by “a”.
Consider a body has velocity
v1 at any instant
t1 and has velocity
v2 at another instant
t2. This change in velocity in time
∆t is called average acceleration.
aav = ∆v/ ∆t
Direction of acceleration is same as velocity.
Unit of acceleration is
ms-2 and is read as meter per second square. Some other common units are
Acceleration at an instant
∆t, which when following the time interval t approaches to zero, is called instantaneous acceleration.
Mathematical form is
ains = limit as ∆t approaches to zero (∆d/∆t)
When a body moves with increasing velocity, then it is said to possess positive acceleration. When a body moves with decreasing velocity, then it is said to possess negative acceleration and this negative acceleration is called Retardation. If a body changes its velocity equally in equal intervals of time, then acceleration produced is said to be constant. Instantaneous acceleration and average acceleration also become equal at constant acceleration.
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