An electron starts from origin at t = 0. The velocity of the electron is 4Πm/s. It moves in an x-y plane under the action of a force that produces a constant acceleration of (4Î + 3ĵ) m/s2. What will be the x-coordinate of the electron when the y-coordinate is 13.5 m?

An electron starts from origin at t = 0. The velocity of the electron is 4Πm/s. It moves in an x-y plane under the action of a force that produces a constant acceleration of (4Î + 3ĵ) m/s2. What will be the x-coordinate of the electron when the y-coordinate is 13.5 m? Correct Answer 40 m

The correct answer is option 1, i.e., 40m.

• The x-coordinate will be 40m when the y-coordinate will be 13.5 m.
• The position of the particle can be calculated using the second equation of motion:
  • s = ut + ½ at²
  • s = 4Î t + ½ (4Î + 3ĵ) t2
  • s = 4Î t + 2Î t² + 1.5ĵ t2
  • s = (4t + 2t²) Î + 1.5t² ĵ
  • x = 4t + 2t²
  • y = 1.5t2 
  • 1.5t2 = 13.5 (given) ⇒ t² = 9 ⇒ t = 3sec
  • x = 4 × 3 + 2 × 3 × 3
  • x = 12 + 18
  • x = 40 m