Looking for NCERT Solutions? Check out here.
An object changing its position with respect to change in time is called motion.
Example: A car moving on the road is said to be in motion.
There are several types of motions:
The motion along straight line is called rectilinear motion.
An object that covers equal distances in equal amount of time is called uniform motion.
An object that covers unequal distances in equal amount of time is called non-uniform motion.
The distance travelled by an object in unit time is called speed. The SI (Standard identity) unit of speed is m s-1 or m/s (metre per second). The formula of speed is:
Speed = distance / time
Formula for Average speed:
Average speed = total distance travelled / total time taken
Or
vav = s / t
Here, vav = average speed
s = total distance travelled
t = total time taken
Velocity is the speed in the definite direction. The SI unit of velocity is m s-1 or m/s. The formula velocity is:
Velocity = displacement / time
Formula for average velocity
Average velocity =( initial velocity + final velocity) / 2
Acceleration is defined as the rate of change of velocity, which means change in the velocity of an object per unit time.
Acceleration = change in velocity / time taken
Or
a = (v - u) / 2
Here, a = acceleration
v = final velocity
u = initial velocity
The following graph will be used to derive all the above equations of motion
Let the initial velocity of an object be u. Its velocity was increased to v with uniform acceleration a in time t.
The acceleration of an object is:
a = change in velocity / time taken
=> a = v – u / t
=> at = v – u
=> at + u = v
Or
=> v = u + at
Let an object travelled total distance s with uniform acceleration a in time t.
The distance travelled by an object is:
Distance = velocity x time
=> s = average velocity x time
=> s = (intial velocity + final velocity) / 2 x time
=> s = (u + v) / 2 x t
=> s = [u + (u + at) /2 ] x t [from I equation of motion, we have v = u + at]
=> s = [(u + u + at) / 2] x t
=> s = (2u + at) /2 x t
=> s = u + at / 2 x t
=> s = ut + ½ at2
Let the object travelled to total distance s with uniform acceleration a in time t.
The distance travelled by an object = the area of OABC
So, distance = area of trapezium OABC
=> s = ½ (sum of || sides) x height
=> s = ½ (OA + OB) X OC
=> s = ½ (u + v) x t
=> s = ½ (u + v) x (v – u)/a [From 1st equation of motion we have, t = v-u/a]
=> s = ½ (v2 – u2) / a
=> s = 1/2a (v2- u2)
=> 2as = v2 – u2