A particle’s velocity varies sinusoidally with time as in the provided graph. Find k in the source expression for its average speed over interval 0 ≤ t ≤ 2π(2n − 1) s, n being any positive integer. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A particle’s velocity varies sinusoidally with time as in the provided graph. Find k in the source expression for its average speed over interval 0 ≤ t ≤ 2π(2n − 1) s, n being any positive integer. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — The average speed for a signed velocity is v̄speed = (1/Δt)∫|v(t)|dt; do not average signed velocity. Step 2 — Divide the stated time window into complete periods and use the absolute area under sinusoidal velocity curve over each period. Step 3 — For v = V₀ sin(ωt), one complete cycle has mean speed 2V₀/π. Step 4 — Compare with the specific prefactor in source; the PDF key is 8. QUALITY FLAG — The graph amplitude, x-axis labels and explicit unknown k are not present in extracted text.