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 acceleration: The velocity v of a particle in a time t is given by the equation v = 10 + 2t^2. We need to find the instantaneous acceleration after 5 seconds. Step 1: Find the acceleration function by differentiating the velocity function with respect to time. Acceleration a(t) is the derivative of velocity v(t) with respect to time t: a(t) = (dv)/(dt) Given v(t) = 10 + 2t^2: a(t) = (d)/(dt)(10 + 2t^2) a(t) = (d)/(dt)(10) + (d)/(dt)(2t^2) a(t) = 0 + 2(2t^2-1) a(t) = 4t Step 2: Calculate the instantaneous acceleration at t = 5s. Substitute t = 5 into the acceleration function: a(5) = 4(5) a(5) = 20m/s^2 Comparing this result with the given options: A. 60m/s^2 B. 15m/s^2 C. 20m/s^2 D. 10m/s^2 The calculated instantaneous acceleration matches option C. The final answer is C. 20 m/s^2.