Answered question

2022-03-21

Answer & Explanation

user_27qwe

user_27qwe

Skilled2023-04-24Added 375 answers

We are given that the distance of a car from a traffic light is given by the function x(t)=bt3-ct2, where b=0.3ms3 and c=0.2ms2. We will calculate the average and instantaneous velocity and acceleration of the car at different times.

(a) To calculate the average velocity of the car from t = 1 to t = 5, we need to find the displacement of the car during this time interval, which is given by x(5) - x(1).
x(5)-x(1)=b(5)3-c(5)2-[b(1)3-c(1)2]
           =b(125)-c(25)-[b(1)-c(1)]
           =37.5-5-0.1
           =32.4m

The time interval is 5 - 1 = 4 s. Therefore, the average velocity of the car is:
average velocity = displacement / time
               =32.44
                = 8.1 m/s

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