This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here's the solution for question 5: Given the displacement S = t^4 + 3t^2 + 4 metres. Step 1: Find the general expression for velocity. Velocity v is the first derivative of displacement with respect to time t. v = (dS)/(dt) = (d)/(dt)(t^4 + 3t^2 + 4) v = 4t^3 + 6t m/s Step 2: Find the general expression for acceleration. Acceleration a is the first derivative of velocity with respect to time t. a = (dv)/(dt) = (d)/(dt)(4t^3 + 6t) a = 12t^2 + 6 m/s^2 a) At t=0 s: Step 3: Calculate displacement, velocity, and acceleration at t=0. • Displacement: S(0) = (0)^4 + 3(0)^2 + 4 = 4 m • Velocity: v(0) = 4(0)^3 + 6(0) = 0 m/s • Acceleration: a(0) = 12(0)^2 + 6 = 6 m/s^2 At t=0: Displacement = 4 m, Velocity = 0 m/s, Acceleration = 6 m/s^2. b) At t=1 s: Step 4: Calculate displacement, velocity, and acceleration at t=1. • Displacement: S(1) = (1)^4 + 3(1)^2 + 4 = 1 + 3 + 4 = 8 m • Velocity: v(1) = 4(1)^3 + 6(1) = 4 + 6 = 10 m/s • Acceleration: a(1) = 12(1)^2 + 6 = 12 + 6 = 18 m/s^2 At t=1: Displacement = 8 m, Velocity = 10 m/s, Acceleration = 18 m/s^2. c) At t=4 s: Step 5: Calculate displacement, velocity, and acceleration at t=4. • Displacement: S(4) = (4)^4 + 3(4)^2 + 4 = 256 + 3(16) + 4 = 256 + 48 + 4 = 308 m • Velocity: v(4) = 4(4)^3 + 6(4) = 4(64) + 24 = 256 + 24 = 280 m/s • Acceleration: a(4) = 12(4)^2 + 6 = 12(16) + 6 = 192 + 6 = 198 m/s^2 At t=4: Displacement = 308 m, Velocity = 280 m/s, Acceleration = 198 m/s^2. That's 2 down. 3 left today — send the next one.