How to measure the Velocity of a moving object by non contact method?

You can make use of two IR detectors. Project the IRs at the path of the bar so that the IR will be cut by the bar as it pass by. Monitor each of that instant with a two channel DSO.

Connect the DSO probes at the IR switch. Catch that instant as the switches turn ON or OFF as the bar cuts the IR. Take the bar travel time from one IR position to the other. Take the distance between the IRs so you can compute the bar velocity(speed).

It can be measured by a series of light gates, with a clock and and a counter. Some bench frequency counters have a stop and start gate for example. Some micro-controllers with counter timers could be arranged to make this measurement. If the clock is 10MHz the resolution of the counter is 0.1uS, and the number of counts between two gates gives the time, and the distance is known. It is important the gates are fast enough in time and precise enough in position to define the start and stop times. LEDs would be fine as a source, but lasers have a more precise beam. A 1mW red laser would probably be good enough. Laser pointers may not be very reliable, but if it is only for an experiment they are fine. The photo-diode detector needs to be fast, to provide output in 0.1us or less. If both are identical some errors cancel out. The trick is to use small PIN diodes with a properly compensated current to voltage converter mounted close to the diode. See fiber optic circuits to get the ideas. If you want really precise you could go up to 100MHz clock or more, but it gets more demanding.

You need to work out the clock rate that suits you. I gave the example to show what can be acieved without too much effort. It may be that 100kHz is fine.

Other gates can be used too. Capacitance, inductance, magnetic are the most likely.

The counter just measures time interval between the start and stop gate. The clock source can be very accurate, so the resolution determines the accuracy. There are other ways, for example a gated integrator using an op-amp. Or an oscilloscope. These will give accuracy from 1% to 0.1%.

A laser doppler speed gun could also work (Police LADAR). It may take a second or two to get a measurement. The speed is something like 10km/h.

Radar.