JEE Main 2023 · 25 January · evening · Single correct · +4 / −1

The distance travelled by a particle is related to time t as x=4t². The velocity of the particle at t=5s is :-

  1. (a) 25 ms⁻¹
  2. (b) 20 ms⁻¹
  3. (c) 8 ms⁻¹
  4. (d) 40 ms⁻¹
Answer and solution

Answer (d) 40 ms⁻¹

Solution

Physics sir · 3 steps

Velocity is the rate of change of position, so differentiate x = 4t² first, then put in t = 5.

  1. Differentiate. Velocity is v = dx/dt. For x = 4t², the power rule gives v = 8t.

    v = d/dt(4t²) = 8t

  2. Put in t. At t = 5 s, v = 8 × 5 = 40 m s⁻¹.
  3. So. The velocity at t = 5 s is 40 m s⁻¹, option (d).

The idea to keep. When position is given as a function of time, velocity is its derivative. Differentiate first, substitute the time last. Never divide x by t unless the velocity is constant.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Rectilinear Motion

Asked about 110 times in JEE Main since 2020. This question is from 2023.