A particle moves in the x-y plane with velocity v = (3t) i-hat + (4t) j-hat m/s. Find the total distance traveled by the particle in 4 seconds.

20 m
40 m
46 m
50 m

Correct answer: 40 m

Solution

Speed = |v| = sqrt((3t)² + (4t)²) = t*sqrt(9+16) = 5t. Since speed is always >= 0, distance = integral₀⁴ 5t dt = 5 * [t²/2]₀⁴ = 5 * 8 = 40 m.

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