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A horizontal floor is coated with a thin oil film. A rectangular block of mass m = 0.4 kg rests on it. At t = 0 an impulse of 1.0 N*s is given to the block, after which it moves along the x-axis with velocity v(t) = v0 * e^(-t/tau), where v0 is constant and tau = 4 s. Find the displacement of the block (in metres) at t = tau. Take e^(-1) = 0.37.

1. 6.3
2. 3.7
3. 2.5
4. 1.6

Correct answer: 6.3

Solution

v0 = 1.0/0.4 = 2.5 m/s, and integrating the exponential decay over one time constant gives about 6.3 m.

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