There are three important equations of motion, that is:
v = u + at
s = ut + 1/2at2
V2 = u2 + 2as
Here ‘u’ is the initial velocity, ‘v’ is the final velocity, ‘a’ is the uniform acceleration and ‘s’ is the displacement of the object. These equations apply to a object moving with a uniform acceleration.
A car moving at a speed of 10 ms-1 comes to rest in 2 seconds. Find its retardation.
In velocity of the car, u = 10 m s-1
Final velocity of the car, v = 0 m s-1
Time taken by the car to come to rest, t = 2s
∴ Acceleration of the car, a = v-u/t = 0 – 10/2 = -5m s-2
Hence, retardation of the car = 5 m s-2.
A bus accelerates uniformly at 8 m s-2 from rest. Find its velocity at the end of 10 seconds.
Given acceleration of the bus, a = 8 s-2.
Initial velocity of the bus, u = 0 m s-1
Time interval, t = 10 s.
∴Final velocity of the car, v = u + at
= 0 + ( 8 ) ( 10 )
= 80 m s-1.
Graphical Representation of Motion
Motion of a object can be represented by graphs . These give the visual representation of motion of the object. There are three types of graphs, that is s – t, v – t and a – t graphs. Here , we discuss s – t and v – t graphs
Displacement – Time Graph
In this graph, displacement is plotted along y-axis and time along x-axis .
|Time in (s)||0||1||2||3||4||5|
|Displacement in (m)||0||5||10||15||20||25|
Significance of Displacement – Time Graph
- Displacement of a particle at any instant of time can be determined.
- Nature of motion of the particle can be studied.
- Slope of the graph at any point gives the instantaneous velocity of the object.
Velocity – Time Graph
If velocity is plotted along y – axis and time along x – axis, then the graph is called v-t graph .
|Time in (min)||0||1||2||3||4||5||6||7||8|
|Velocity in ( m s-1)||5||10||15||20||20||20||15||10||5|
Significance of V – T Graph
- Nature of motion of object can be determined.
- Slope of the linear part of the curve gives the acceleration,
- Are under the curve gives the displacement of the object.
- Velocity at any instant can be found out.