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Time intervals x = 4cos( π t)

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Time intervals

x = 4cos(π t)

Find the time interval between the 1st and 2nd time the particle is at x = 3.

x = 3 so 3 = 4cos π t

= cos π t

so π t = 0.7227 or 2π – 0.7227

So t = 0.153 or 1.180 s so time interval is 1.03 s

x = 4cos π t

Find the time interval between the 2nd and 3rd time the particle has speed 15m/s.

Differentiating, v = –6π sin( π t)

The graph shows when the speed is 15m/s.

±15 = –6π sin( π t)

π t = 0.9203 or π – 0.9203 or π + 0.9203

So t = 0.195, 0.471, 0.862 s

The time interval between the 2nd and 3rd time the particle has speed 15m/s is 0.391s.