**Problem 5:** A proton is moving with a speed of 1 × 10^{7} m/s, passes
through a 0.020 cm thick sheet of paper and emerges with a speed of 2.0 × 10^{6}
ms^{-1}. Assuming uniform deceleration, find retardation and time taken
to pass through the paper.

**Solution**

**Given:** v_{i} = 1 × 10^{7} ms^{-1}, Thickness = distance = s = 0.02 cm = 0.02 × 10^{-2} m,

v_{f} = 2.0 × 10^{6} ms^{-1}

**Find:** Deceleration
a and time t

To find the required quantities, we use equation of motion,

Put the values

This equation gives the deceleration of proton.

To find the time
taken to pass through the paper, we use equation of motion v_{f} = v_{i}
+ at. Put values,

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