Average acceleration

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Acceleration is the rate of change of velocity but Average acceleration is the ratio of average velocity and the average time interval.

          Average acceleration = Δv/Δt

Or,    Average acceleration = (vf – vi)/(tf – ti)

Where, Δv = change in velocity

          Δt = change in time

          Vf = final velocity

          Vi = initial velocity

          tf = final time

and   ti = initial time

Unit of average acceleration is same as acceleration that is m/s.

If a bike moves from the rest to 6 m/s in 3 sec. its average acceleration will be 6/3 = 2 m/s.

Example: A honey bee accelerate to 10 m/s from 4 m/s in 3s. Calculate its average acceleration?

Solution: Given that,
          Initial velocity = 4 m/s
          Final velocity = 10 m/s
And   time elapsed = 3 sec
We have the equation for the average acceleration,
          Average acceleration, a = (vf – vi)/t = (10 – 4)/3 = 6/3 = 2 m/s
 

Example: At 10:30, a rocket begins to accelerate from 50 mph. At 10:45 the rocket is travelling at 300 mph. What is the acceleration of the rocket?

Solution: Given that,
                   Initial velocity = 50 mph
                   Final velocity = 300 mph
                   Initial time = 10:30
                   Final time = 10:45
          Difference of time = (10:45 – 10:30) = 15 min = 15/60 hr = 0.25 hr
So, average acceleration = (300 – 50)/(10:45 – 10:30)
                                      = 250/0.25
                                      = 1000 mph^2


 

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