"Deceleration" is a decrease in speed, however you are still going in the SAME direction so it is POSITIVE.
"Retardation" is going in the OPPOSITE direction, therefore it is NEGATIVE.
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Retardation or deceleration is negative accelaration formula for finding retardation is same as that of accelaration: v-u/t, where v is the final velocity, u is the initial velocity and t is the time taken. eg- a bus is travelling at 20 m/s. Brakes are applied to stop the bus. The total time taken by the bus to stop is 2 s. Find its retardation. ans- v=0; u=20; t=2 accelaration= 0-20/2 a= -10 m's^2 retardation= 10 m/s^2 (because retardation is negative accelaration)
Retardation = change in vel / time taken
Retardation is the opposite of acceleration.It starts from a non zero uniform velocity.For this to happen any velocity (not zero) of a vehicle should go on decreasing.The rate of decreasing may be anything.If it is decreasing then that is retardation.
In a controlled test condition (like crash tests on cars) an accelerometer is used to measure the rate of deceleration. It should be possible to estimate the deceleration following a collision if the speed of the vehicles at the moment of the collision is known. We could do this by measuring the amount the car was crushed/dented during the collision. We know the vehicle decelerated from its starting speed over this distance so we can estimate the average deceleration. I believe there are more sophisticated techniques used by accident investigators. As an aside, in strict physics terminology, slowing down (as well as any other change in velocity) is acceleration, not deceleration however deceleration is often used to imply a reduction in speed in every day English. If you want to get into this further have a look at "Are speed and velocity the same?" and remember that acceleration is also a vector.
Calculate the gradient of the curve which will give the acceleration. Change the sign of the answer to convert acceleration into retardation.