A car is traveling on a straight road with an initial velocity of 22.0 m/s due east. What is the final velocity of the car two minutes later if its average acceleration is 0.14 m/s² due west? Determine both the magnitude and direction of the final velocity.

a) 38.8 m/s due east
b) 5.2 m/s due east
c) 5.2 m/s due west
d) 38.8 m/s due west

Question

14-05-2025
Physics

High School

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A car is traveling on a straight road with an initial velocity of 22.0 m/s due east. What is the final velocity of the car two minutes later if its average acceleration is 0.14 m/s² due west? Determine both the magnitude and direction of the final velocity.

a) 38.8 m/s due east
b) 5.2 m/s due east
c) 5.2 m/s due west
d) 38.8 m/s due west

Answer :

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prakasht3400 prakasht3400 · Answer 1 · 2024-09-28T07:12:59-04:00

Final answer:

By using the formula v = u + at and converting time to seconds, the final velocity of the car is calculated to be 5.2 m/s due east after two minutes with a 0.14 m/s² acceleration due west. Therefore, the correct option is b, 5.2 m/s due east.

Explanation:

The final velocity of the car can be calculated using the formula for velocity which involves initial velocity, acceleration, and time: v = u + at, where 'v' is the final velocity, 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time.

The car's initial velocity is given as 22.0 m/s due east, and it has an average acceleration of 0.14 m/s2 due west. Since acceleration is opposite to the direction of the velocity, it will reduce the car's speed. First, convert time from minutes to seconds: 2 minutes = 2 * 60 = 120 seconds.

Now, plug in the values: v = 22.0 m/s - (0.14 m/s2 * 120 s). Calculate the change in velocity: 0.14 m/s2 * 120 s = 16.8 m/s. Calculate the final velocity: 22.0 m/s - 16.8 m/s = 5.2 m/s due east. The car is still moving to the east since the change in velocity is less than the initial velocity. Therefore, the correct option is b, 5.2 m/s due east.