Describe the position of an object we need to specify a reference point called the origin.
An object may appear to be moving for one person and stationary for some other. For the passengers in a moving bus, the roadside trees appear to be moving backwards. Most motions are complex. Some objects may move in a straight line, others may take a circular path. Some may rotate and a few others may vibrate. There may be situations involving a combination of these.
The simplest type of motion is the motion along a straight line.
There are certain quantities which are described by specifying only their numerical values. The numerical value of a physical quantity is its magnitude.
When the object covers equal distances in equal intervals of time, it is said to be in uniform motion. The time interval in this motion should be small.
When the objects cover unequal distances in equal intervals of time, for example, when a car is moving on a crowded street or a person is jogging in a park. These are some instances of non-uniform motion.
The different objects may take different amounts of time to cover a given distance. Some of them move fast and some move slowly. The rate at which objects move can be different. Also, different objects can move at the same rate. One of the ways of measuring the rate of motion of an object is to find out the distance travelled by the object in unit time.
The SI unit of speed is metre per second. This is represented by the symbol m s—1 or m/s. The other units of speed include centimetre per second (cm s—1) and kilometer per hour (km h—1). To specify the speed of an object,
The average speed of an object is obtained by dividing the total distance travelled by the total time taken. That is,
Average speed = Total distance travelled/Total time taken
If an object travels a distance s in time t then its speed v is,
v = s/t
The rate of motion of an object can be more comprehensive if we specify its direction of motion along with its speed. The quantity that specifies both these aspects is called velocity.
Velocity is the speed of an object moving in a definite direction. The velocity of an object can be uniform or variable. It can be changed by changing the object's speed, direction of motion or both.
In case the velocity of the object is changing at a uniform rate, then average velocity is given by the arithmetic mean of initial velocity and final velocity for a given period of time. That is,
Average velocity = initial velocity + final velocity/2
Mathematically, vav = u + v/2
Where vav is the average velocity, u is the initial velocity and v is the final velocity of the object.
Speed and velocity have the same units, that is, m s—1 or m/s.
During uniform motion of an object along a straight line, the velocity remains constant with time. In this case, the change in velocity of the object for any time interval is zero. the change in velocity of the object during any time interval is not zero.
Acceleration is a measure of the change in the velocity of an object per unit time.
Acceleration = change in velocity/time taken
If the velocity of an object changes from an initial value u to the final value v in time t, the acceleration a is,
a = v — u/t
The acceleration is taken to be positive if it is in the direction of velocity and negative when it is opposite to the direction of velocity. The SI unit of acceleration is m s—2 .
An object can travel with non-uniform acceleration if its velocity changes at a non-uniform rate.
Graphs provide a convenient method to present basic information about a variety of events.
To describe the motion of an object, we can use line graphs. In this case, line graphs show dependence of one physical quantity, such as distance or velocity, on another quantity, such as time.
The change in the position of an object with time can be represented on the distance-time graph adopting a convenient scale of choice.
The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graph.
When an object moves along a straight line with uniform acceleration, it is possible to relate its velocity, acceleration during motion and the distance covered by it in a certain time interval by a set of equations known as the equations of motion.
v = u + at
s = ut + 1/2at2
2 a s = v2 — u2
Where u is the initial velocity of the object which moves with uniform acceleration a for time t, v is the final velocity, and s is the distance travelled by the object in time t.
Consider the velocity-time graph of an object that moves under uniform acceleration.
The distance travelled by the object is obtained by the area enclosed within OABC under the velocity-time graph AB.
Thus, the distance s travelled by the object is given by
s = area OABC (which is a trapezium)
= area of the rectangle OADC + area of the triangle ABD
When the velocity of an object changes, we say that the object is accelerating. The change in the velocity could be due to change in its magnitude or the direction of the motion or both.
The motion of the athlete moving along a circular path is, therefore, an example of an accelerated motion. We know that the circumference of a circle of radius r is given by 2pr . If the athlete takes t seconds to go once around the circular path of radius r, the speed v is given by
v = 2 Πr/t
When an object moves in a circular path with uniform speed, its motion is called uniform circular motion.