A particle moves along a line with position s(t) = αt² - βt + γ, where α = 1 m s⁻², β = 6 m s⁻¹ and γ = 5 m. Find its average speed (m s⁻¹) from t = 0 to t = 6 s.
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Question

A particle moves along a line with position s(t) = αt² − βt + γ, where α = 1 m s⁻², β = 6 m s⁻¹ and γ = 5 m. Find its average speed (m s⁻¹) from t = 0 to t = 6 s.

G1 Physics · Accepted Answer

Step 1: Substitute the constants: s(t) = t² − 6t + 5 (metres). Step 2: Velocity v = ds/dt = 2t − 6; therefore the particle reverses direction at t = 3 s. Step 3: Positions: s(0) = 5 m, s(3) = −4 m and s(6) = 5 m. Step 4: Total distance = |−4 − 5| + |5 − (−4)| = 9 + 9 = 18 m. Step 5: Average speed = total distance/time = 18/6 = 3 m s⁻¹. Final answer: 3 m s⁻¹ (Option C).