# speeding up and Uniform speeding up

It is defined as the rate of velocity. If the speed is increasing then speeding up is positive and its direction is in the direction of motion.

however if the speed is decreasing then the speeding up is negative. The negative speeding up is called retardation.

Now consider another example of an object moving on a curved path with uniform speed.

Here the change in velocity is not due to change in speed but due to change in direction. The direction of speeding up in this example of circular motion is perpendicular to the direction of motion.

speeding up can be calculated with the following mathematical equation:

speeding up = Change in velocity————-Time interval

a–> = –> ^V—-^t

or

a–> = –>Vf — –>Vi ——— ^t

where a–> is the speeding up, Vi–> is the initial velocity, Vf–> is the final velocity and ^t is the time interval.

speeding up is a vector quantity, as it is completely stated by giving extent in addition as direction. The unit of speeding up in SI system is metre/second2, i.e.,,/s2 or ms-2.

Uniform speeding up

If the velocity of a body moving a long a straight line changes uniformly in equal intervals of time, however short the interval may be, the speeding up so produced is called uniform speeding up.

Average speeding up

The ration between total change in velocity and time is called average speeding up.

Aav = –>^V—^t

Example

The velocity of a car moving along a road increases from 10 m/s to 60m/s in 20s. Fine its average speeding up.

Solution

Initial velocity of the car, Vi = 10m/s.

Final velocity of the car, Vf = 60 m/s.

Chane in velocity, ^V= 60m/s

Time, ^t = 20 s

Average speeding up Aav = ^V—-t

= 50m/s——20s = 2.5 m/s2

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