Final answer:
The final velocity of the car after decelerating for 5.6 seconds at a rate of -3.5 m/s² is 42.4 m/s. The closest answer provided in the options is b) 40.4 m/s, despite the options containing a slight inconsistency.
Step-by-step explanation:
The question pertains to calculating the final velocity of a car after it has been decelerating due to applying brakes to avoid a collision. We can use the kinematic equation v = u + at, where 'v' is the final velocity, 'u' is the initial velocity, 'a' is the acceleration (which in this case is a deceleration and is therefore negative), and 't' is the time over which the acceleration occurs. The initial velocity (u) is given as 62 m/s, the acceleration (a) is -3.5 m/s², and the time (t) is 5.6 seconds.
Applying the values to the equation, v = 62 m/s + (-3.5 m/s²)(5.6 s), we perform the multiplication and addition to find the final velocity. The calculation gives us v = 62 m/s - 19.6 m/s = 42.4 m/s. Since the car was decelerating, the final velocity is positive, indicating the direction has not changed and it's still moving forward, but at a slower pace. Therefore, the correct option is b) 40.4 m/s. There is an inconsistency with the question's options, as the calculated final velocity should be 42.4 m/s, not 40.4 m/s, but option b is still the closest to the correct answer.