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NEET generalGeneralHard

Question

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E\vec{E}. Due to the force qEq\vec{E}, 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

1 m/s, 3.5 m/s

2

1 m/s, 3 m/s

3

2 m/s, 4 m/s

4

1.5 m/s, 3 m/s

Step-by-Step Solution

Acceleration a=v/t=6/1=6 m/s2a = v/t = 6/1 = 6 \text{ m/s}^2. At t=1t=1s, v=6v=6 m/s. For t=1t=1 to 33s, a=6 m/s2a' = -6 \text{ m/s}^2. Velocity at t=3t=3s is v3=6+(6)(2)=6v_3 = 6 + (-6)(2) = -6 m/s. Displacement s=s1+s2=12(6)(1)+[6(2)+12(6)(22)]=3+[1212]=3s = s_1 + s_2 = \frac{1}{2}(6)(1) + [6(2) + \frac{1}{2}(-6)(2^2)] = 3 + [12 - 12] = 3 m. Average velocity = 3/3=13/3 = 1 m/s. Distance d=d1+d2=3+1212=3+6=9d = d_1 + d_2 = 3 + |12 - 12| = 3 + 6 = 9 m. Average speed = 9/3=39/3 = 3 m/s.

Exam Context & Concepts Covered

This question aligns with the NEET general syllabus, specifically targeting concepts from General. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

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