What is acceleration ?
A particle moving with variable velocity is said to possess acceleration. When a particle executes non-uniform motion, its velocity changes. Acceleration is defined as the rate of change of velocity.
Acceleration = Change in velocity ⁄ time
Thus, mathematically acceleration ,
a = v−u ⁄ t
Where ‘u’ is the initial velocity, v is the final velocity
Velocity – it is displacement of a body in unit time or rate of displacement.
Velocity = displacement / time
A car moves along a straight path with variable velocity as shown in the figure. When the car is at position A, its velocity is 10 m s−1 and when it is at position B, its velocity is 20 m s−1. If the car takes 5 seconds of time to move from A to B, find the acceleration of the car.
Initial position of the car at position A = u = 10 m s−1
Final velocity of the car at position B = v = 20 m s−1
The change in velocity of the car, Δv = v = 20 m s−1 −10m s−1 = 10 m s−1
The time taken for the car to move from A to B, Δt = 5 s
∴ Acceleration of the car, a = Δv/Δt = 10 m s−1 = 2 m s-2
Acceleration important point
- Since velocity is a vector, acceleration is also a vector.
- Unit of acceleration is cm s−2 in C.G.S. system and m s−2 in S.I. system.
- If the velocity of the particle increases with respect to time, (v > u), the acceleration is said to be positive.
- If the velocity of the particle decreases with respect to time, the acceleration is said to be negative, and is referred to as’ deceleration or ‘retardation’.
- When the motion of a particle is such that there are equal changes in velocity in equal intervals of time, then it is said to be moving with ‘uniform acceleration‘, e.g., a body falling under the influence of gravity.
- The acceleration of a body falling under the influence of Earth’s gravitational force is called ‘acceleration due to gravity’ and is represented by the letter ‘g’.
- The direction of the acceleration due to gravity is always downward (towards and normal to the surface of Earth). The magnitude of ‘g’ varies from place to place but is constant at a given place. The average value of ‘g’ at sea level is 9.8 m s−2 in S.I. system and 980 cm s−2 in C.G.S. system.
- When a body moves with uniform acceleration, its average Velocity can be calculated by using the expression, Vaverage = u+ v/2 where ‘u’ and y are its initial 2. And final velocities for a given time interval