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NEET PHYSICSELECTRIC CHARGES AND FIELDSMedium

Question

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force qE, its velocity increases from 0 to 6 m/s in a 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:

A

2 m/s, 4 m/s

B

1 m/s, 3 m/s

C

1 m/s, 3.5 m/s

D

1.5 m/s, 3 m/s

Step-by-Step Solution

  1. 0 to 1 sec: Initial velocity u=0u=0, Final velocity v=6v=6 m/s. Acceleration a=(6−0)/1=6a = (6-0)/1 = 6 m/s². Displacement S1=12at2=12(6)(1)2=3S_1 = \frac{1}{2}at^2 = \frac{1}{2}(6)(1)^2 = 3 m. Distance d1=3d_1 = 3 m.
  2. 1 to 3 sec: Field reverses, so acceleration a′=−6a' = -6 m/s². Initial velocity for this interval u′=6u' = 6 m/s. Duration t′=2t' = 2 s.
  • Displacement S2=u′t′+12a′(t′)2=6(2)+12(−6)(2)2=12−12=0S_2 = u't' + \frac{1}{2}a'(t')^2 = 6(2) + \frac{1}{2}(-6)(2)^2 = 12 - 12 = 0 m.
  • To find distance, check if particle stops. v=u′+a′t⇒0=6−6t⇒t=1v = u' + a't \Rightarrow 0 = 6 - 6t \Rightarrow t=1 s. So it stops at total time t=2t=2 s and reverses.
  • Distance forward (1s to 2s): dfwd=6(1)−3(1)2=3d_{fwd} = 6(1) - 3(1)^2 = 3 m.
  • Distance backward (2s to 3s): Magnitude of displacement for remaining 1s = 3 m.
  • Total distance d2=3+3=6d_2 = 3 + 3 = 6 m.
  1. Averages (0 to 3 sec):
  • Total Displacement = S1+S2=3+0=3S_1 + S_2 = 3 + 0 = 3 m.
  • Total Distance = d1+d2=3+6=9d_1 + d_2 = 3 + 6 = 9 m.
  • Average Velocity = 3 m/3 s=13 \text{ m} / 3 \text{ s} = 1 m/s.
  • Average Speed = 9 m/3 s=39 \text{ m} / 3 \text{ s} = 3 m/s.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from ELECTRIC CHARGES AND FIELDS. 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.

PHYSICSELECTRIC CHARGES AND FIELDSchargefrictionlesshorizontalsurfaceinfluence

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