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A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E⃗. Due to the force qE⃗, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively

1. 2 m/s, 4 m/s
2. 1 m/s, 3 m/s
3. 1.5 m/s, 3 m/s
4. 1 m/s, 3.5 m/s

Correct answer: 1 m/s, 3 m/s

Solution

The car accelerates uniformly under the electric field for 1 second, reaching 6 m/s. When the field reverses, it decelerates uniformly for 2 seconds, coming to rest after 1 second and then moving in the opposite direction for another second, reaching -6 m/s. The displacement is 6 m forward in the first second, 3 m backward in the next 2 seconds, giving a net displacement of 3 m. The average velocity is 3 m / 3 s = 1 m/s. The total distance traveled is 6 m + 3 m = 9 m, so the average speed is 9 m / 3 s = 3 m/s.

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