Acceleration of a body may be defined as the time rate of change velocity. If the velocity of a body is changing then it is said to posses acceleration.
Acceleration = change of velocity / time
If the velocity of a body is increasing, then its acceleration will be positive and if the velocity of a body is decreasing, then its acceleration will be negative. Negative acceleration is also called retardation.
Acceleration is a vector quantity and its unit in S.I system is meter per second per second. (m/sec2 OR m.sec-2)
Average acceleration is defined as the ratio of the change in velocity of a body and the time interval during which the velocity has changed.
Suppose that at any time t1 a body is at A having velocity V1. At a later time t2, it is at point B having velocity V2. Thus,
Change in Velocity = V2 – V1 = Δ V
Time during which velocity has changed = t2 – t1 = Δ t
It is defined as the acceleration of a body at a certain instant
a(ins) = lim Δ V / Δ t
where Δt → 0 is read as “Δt tends to zero”, which means that the time is very small.
Acceleration from Velocity – Time Graph
We can determine the acceleration of a body by velocity – time graph such that the time is taken on x-axis and velocity on y-axis.
Equations of Uniformly Accelerated Rectilinear Motion
There are three basic equations of motion. The equations give relations between
Vi = the initial velocity of the body moving along a straight line.
Vf = the final velocity of the body after a certain time.
t = the time taken for the change of velocity
a = uniform acceleration in the direction of initial velocity.
S = distance covered by the body.
1. Vf = Vi + a t
2. S = V i t + 1/2 a t2
3. 2 a S = V f2 – V i 2
Motion Under Gravity
The force of attraction exerted by the earth on a body is called gravity or pull of earth. The acceleration due to gravity is produced in a freely falling body by the force of gravity. Equations for motion under gravity are
1. Vf = Vi + g t
2. S = V i t + 1/2 g t2
3. 2 g S = Vr2 – Vi2
where g = 9.8 m / s2 in S.I system and is called acceleration due to gravity.
Law of Motion
Isaac Newton studied motion of bodies and formulated three famous laws of motion in his famous book “Mathematical Principles of Natural Philosophy” in 1687. These laws are calledNewton’s Laws of Motion.