How to measure the acceleration of motor?

To the best of my knowledge, I don't think there is a machine available for that purpose. But yeah, I believe it can be done by measuring the current.

A motor takes high starting current and slowly this current decreases to the rated value once the motor attains the rated speed. The rated current and rated speed of motor are available from the name plate. With the help of an ammeter and a stop watch I think we can measure the acceleration.

Measure the time required for the current to decrease to rated value from the instant of switching the motor ON. Now the initial speed is 0 RPM and final speed is rated RPM. Time taken to reach 0 to rated RPM is measured. So now the acceleration can be found out by (rated rpm - 0)/time. A few repetative measurements and its average should give a descent value I believe.

why you need to measure acceleration ?? u can measure the speed with tachometer and with algberaic operation with time u can measure the acceleration ?

Ordinary tachometers doesn't give an instantaneous feed back. It takes some time for the meter to calculate and display the rpm. Well it depends on what type of meter is being used, still. That should bring a fair amount of error, depending on the speed of meter response.