A point particle moves along a given x-axis with the law of motion x(t) = 4 cos(ωt) where x is in metres, t in seconds and ω = 2π rad/s. The velocity of the point particle at the instant t* = 1/2 s equals:
A) approximately −4 m/s
B) approximately 4,2 m/s
C) approximately 25,1 m/s
D) approximately 8,5 m/s
E) 0 m/s
IMAT 2024 · Question 59
Q59 - Harmonic motion
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The correct answer is E) 0 m/s.
Velocity is the derivative of position: v = −4ω sin(ωt).
At t = 1/2 s with ω = 2π, ωt = π and sin π = 0, so v = 0.
That makes sense: at that moment x = 4 cos π = −4 m, the far end of the swing, where the particle stops for an instant before coming back. 25.1 m/s (4 × 2π) is the top speed, which it only reaches in the middle.
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