KINEMATICS - SPEED AND VELOCITY
VELOCITY
Velocity is defined as a rate of change of displacement. In a simple, velocity specifies speed of body and its direction. The speed of a car traveling north on a major freeway and the speed of a rocket launching into space can both be measured using velocity.
Velocity Formula:
The most common way to calculate the constant velocity of an object moving in a straight line is with this formula:
\(V={ d \over t}\) \(V = \frac{d}{t}\)
V is the velocity
d is the displacement
t is the time it takes to complete the movement
Units of Velocity:
The SI (international) units for velocity are m/s (metre per second), but velocity may also be expressed in any units of distance per time. Other units include miles per hour (mph), kilometre per hour (kph), and kilometre per second (km/s).
1 km/hr = 5/18 m-s-1
Types of Velocity:
T here are four types of speed and they are:
1. Uniform velocity 2. Non-Uniform velocity
3. Average velocity 4. Instantaneous velocity
Uniform velocity:
It is the condition in which a body covers equal distance in equal interval of the time in a specified direction.
Ex: The rotation of Moon around the earth etc.
Non-Uniform Velocity:
When a body covers unequal distances in equal intervals of time in a specified direction or equal distances in equal intervals of time, but its direction changes then body is said to be moving with non-uniform velocity.
Ex: A car moving on the road etc.
Average velocity:
The average velocity of a body in a certain time interval is given as the displacement of the body in that time interval divided by time. So if a particle covers a certain displacement A!B in a time t1 to t2, then the average velocity of the particle is:
\({\overrightarrow V _{av}} = \frac{{\overline {AB} }}{{{t_2} - {t_1}}}\)
In general, formula is:
\(Average\,\,velocity\,\, = \frac{{Total\,Displacement}}{{Total\,time}}\)
Understand the concept average velocity through the examples given below.
Ex:A particle has covered a distance of 1000 meters and a displacement of 200 meters in 1 min 40 sec. Find the Speed and Velocity of the particle during motion
Solution
Time Taken = 1 min 40 sec = 100 sec
Speed = Distance/ Time
Speed = 1000/ 100 = 10 m/sec
Velocity = Displacement/ Time
Velocity = 200/100 = 2 m/sec
Example 2:
Calculate the average velocity at a particular time interval of a person if he moves 7 m in 4 sec and 18 m in 6 sec along x-axis?
Solution:
Initial distance traveled by the person Xi = 7 m,
Final distance traveled Xf= 18 m,
Initial time interval Ti = 4 sec
Final time interval Tf = 6 sec
Average velocity.\({V_{avg}} = \frac{{{X_f} - {X_i}}}{{{T_f} - {T_i}}} = \frac{{18 - 7}}{{6 - 4}} = 5.5m/sec\)
Instantaneous velocity:
In simple words, the velocity of an object at that instant of time. Instantaneous velocity definition is given as ”The velocity of an object under motion at a specific point of time.”
If the object possesses uniform velocity then the instantaneous velocity may be the same as its standard velocity.
We know that the average velocity for a given time interval is total displacement divided by total time. As this time interval approaches zero, the displacement also approaches zero. The ratio of displacement to time is non zero and is called instantaneous velocity.
Unit of Instantaneous Velocity:
The SI unit of instantaneous velocity is m/s. It is a Vector quantity.
Example 3:If the object moves with a constant standard velocity of 50 km/hr for two hours. What is its instantaneous velocity after 30 minutes from the time it started?
Solution:
Instantaneous velocity of the object is 50 km/hr. As the object is under uniform velocity, its instantaneous velocity is the same as its standard velocity.