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 the instantaneous velocity: The equation for the acceleration of a particle is given by a = 2 + 2t. We need to find the instantaneous velocity after 4 seconds. Step 1: Integrate the acceleration function to find the velocity function. Velocity v(t) is the integral of acceleration a(t) with respect to time t: v(t) = a(t)\,dt Given a(t) = 2 + 2t: v(t) = (2 + 2t)\,dt v(t) = 2\,dt + 2t\,dt v(t) = 2t + 2((t^2)/(2)) + C v(t) = 2t + t^2 + C Here, C is the constant of integration, representing the initial velocity v(0). Since no initial velocity is given, we assume the particle starts from rest, meaning v(0) = 0. Substituting t=0 and v(0)=0: 0 = 2(0) + (0)^2 + C C = 0 So, the velocity function is: v(t) = 2t + t^2 Step 2: Calculate the instantaneous velocity at t = 4s. Substitute t = 4 into the velocity function: v(4) = 2(4) + (4)^2 v(4) = 8 + 16 v(4) = 24m/s Comparing this result with the given options: A. 8m/s B. 32m/s C. 24m/s D. 42m/s The calculated instantaneous velocity matches option C. The final answer is C. 24 m/s.