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JEE MainPhysicsMotion in One Dimension

A speedboat moving on a lake starts decelerating uniformly. After 2 s of deceleration, its velocity is 40 m s ⁻¹ . After a total of 3.5 s of deceleration, its velocity is 10 m s ⁻¹ . The initial velocity of the speedboat before it started decelerating is

Options

  1. A60 m s ⁻¹
  2. B70 m s ⁻¹
  3. C80 m s ⁻¹
  4. D0 m s ⁻¹

Correct answer

C. 80 m s ⁻¹

Step-by-step solution

Let the initial velocity of the speedboat be u and its constant acceleration be a . Using the first equation of motion, v = u + at , we can write the velocity at t = 2 s as: 40 = u + 2a (1) Similarly, the velocity at t = 3.5 s is: 10 = u + 3.5a (2) Subtracting equation (1) from equation (2) gives: 10 - 40 = (u + 3.5a) - (u + 2a) -30 = 1.5a a = -20 m s ⁻² Substitute the value of a back into equation (1): 40 = u + 2(-20) 40 = u - 40 u = 80 m s ⁻¹ The initial velocity of the speedboat is 80 m s ⁻¹ . Answer: 80 m s ⁻¹

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