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
The displacement of the particle is given by S = 6 + 10t - t^2. a) The distance travelled from t=1 to t=4 Step 1: Find the velocity function by differentiating the displacement function with respect to time. V = (dS)/(dt) = (d)/(dt)(6 + 10t - t^2) = 10 - 2t Step 2: Determine if the particle changes direction within the interval t=1 to t=4 by finding when the velocity is zero. Set V = 0: 10 - 2t = 0 2t = 10 t = 5 s Since t=5 is outside the interval [1, 4], the particle does not change direction during this time. Therefore, the distance travelled is the magnitude of the displacement between t=1 and t=4. Step 3: Calculate the displacement at t=1 and t=4. At t=1: S(1) = 6 + 10(1) - (1)^2 = 6 + 10 - 1 = 15 m At t=4: S(4) = 6 + 10(4) - (4)^2 = 6 + 40 - 16 = 30 m Step 4: Calculate the distance travelled. Distance travelled = |S(4) - S(1)| = |30 - 15| = 15 m The distance travelled from t=1 to t=4 is 15 m. b) The velocity when t=6 Step 1: Use the velocity function found in part a). V = 10 - 2t Step 2: Substitute t=6 into the velocity function. V(6) = 10 - 2(6) = 10 - 12 = -2 m/s The velocity when t=6 is -2 m/s. Send me the next one 📸