A cart is slowing down at a rate of 2t+60 centimeters per second per second (where t is the time in seconds). By how many centimeters per second does the cart slow down between t=5 and t=15 ? Choose 1 answer: (A) 20 (B) 75 (C) 800 (D) 875

Question

A cart is slowing down at a rate of  2t+60 centimeters per second per second (where  t is the time in seconds). By how many centimeters per second does the cart slow down between  t=5 and  t=15 ? Choose 1 answer: (A) 20 (B) 75 (C) 800 (D) 875

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We are given an acceleration function in terms of time, which is 2t + 60 cm/s^2. We need to find the change in velocity between t=5 and t=15 seconds.Calculate acceleration at t=5: Calculate the acceleration at t=5 seconds. Acceleration at t=5 is a(5) = 2(5) + 60 = 10 + 60 = 70 cm/s^2.Calculate acceleration at t=15: Calculate the acceleration at t=15 seconds. Acceleration at t=15 is a(15) = 2(15) + 60 = 30 + 60 = 90 cm/s^2.Calculate average acceleration: Calculate the average acceleration between t=5 and t=15 seconds. The average acceleration is the sum of the accelerations at t=5 and t=15 divided by 2. Average acceleration = (a(5) + a(15)) / 2 = (70 + 90) / 2 = 160 / 2 = 80 cm/s^2.Calculate time interval: Calculate the time interval between t=5 and t=15 seconds. The time interval Δt is t_final - t_initial = 15 - 5 = 10 seconds.Calculate change in velocity: Calculate the change in velocity using the average acceleration and the time interval. Change in velocity Δv = average acceleration * time interval = 80 cm/s^2 * 10 s = 800 cm/s.

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