This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
ScanSolve AI Answer
Okay, Godans..acc, let's solve this in English. Given the displacement of a particle S = t^3 - 5t^2 + 3t + 4, where t is time in seconds. a) Find the displacement of the particle when t=5. Step 1: Substitute t=5 into the displacement formula. S = t^3 - 5t^2 + 3t + 4 S(5) = (5)^3 - 5(5)^2 + 3(5) + 4 S(5) = 125 - 5(25) + 15 + 4 S(5) = 125 - 125 + 15 + 4 S(5) = 19 The displacement of the particle when t=5 is 19 m. b) Find the velocity of the particle when t=5. Step 1: Find the velocity formula (V) by differentiating the displacement formula (S) with respect to t. V = (dS)/(dt) = (d)/(dt)(t^3 - 5t^2 + 3t + 4) V = 3t^2 - 10t + 3 Step 2: Substitute t=5 into the velocity formula. V(5) = 3(5)^2 - 10(5) + 3 V(5) = 3(25) - 50 + 3 V(5) = 75 - 50 + 3 V(5) = 28 The velocity of the particle when t=5 is 28 m/s. c) Find the values of t when the particle is momentarily at rest. Step 1: The particle is at rest when its velocity is zero (V=0). Set the velocity formula equal to zero. 3t^2 - 10t + 3 = 0 Step 2: Solve the quadratic equation for t. 3t^2 - 9t - t + 3 = 0 3t(t - 3) - 1(t - 3) = 0 (3t - 1)(t - 3) = 0 Therefore, 3t - 1 = 0 3t = 1 t = (1)/(3) seconds. Or t - 3 = 0 t = 3 seconds. The values of t when the particle is momentarily at rest are t = (1)/(3) s or t = 3 s. d) Find the acceleration of the particle when t=2. Step 1: Find the acceleration formula (A) by differentiating the velocity formula (V) with respect to t. A = (dV)/(dt) = (d)/(dt)(3t^2 - 10t + 3) A = 6t - 10 Step 2: Substitute t=2 into the acceleration formula. A(2) = 6(2) - 10 A(2) = 12 - 10 A(2) = 2 The acceleration of the particle when t=2 is 2 m/s^2. That's 2 down. 3 left today — send the next one.