Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEET2007PhysicsMotion in One DimensionActual

The position x of a particle with respect to time t along x -axis is given by x=9 t^2-t^3 where x is in metres and t in second. What will be the position of this particle when it achieves maximum speed along the +x direction?

Options

  1. A54 ~m
  2. B81 ~m
  3. C24 ~m
  4. D32 ~m .

Correct answer

A. 54 ~m

Step-by-step solution

It is given that aligned x & =9 t^2-t^3 v & = d x d t =18 t-3 t^2 d v d t & =a=18-6 t aligned for maximum speed d v d t =0 and d^2 v d t^2 negative So 18-6 t=0 t=3 s at t=3 s, x=9(3)^2-(3)^3=81-27=54 ~m

Practice Motion in One Dimension on Quantrex Academy →

More from Motion in One Dimension

A vehicle runs on a straight road of length 'L'. It travels half the distance with speed V and the remaining distance with speed 3V 2 . Its average speed is 2026For uniform acceleration in linear motion which of the following is NOT CORRECT ? 2026Two cars, P and Q move toward each other, getting 8 m closer every second. If they move in the same direction, they get 0.6 m closer every second. If car P is faster than car Q the 2026A block is kept on the floor of an elevator at rest. The elevator starts descending with acceleration of 5 m/s ^2 . The displacement of the block during the first 0.2 s after the s 2026The acceleration ( a ) -time ( t ) graph for the body starting from rest is as shown in the figure. The maximum speed of the body is 2026A train accelerates from rest at a constant rate 'p' for some time (attains velocity 'v') and then retards to rest at the constant rate 'q'. If the total distance covered by the tr 2026The following plots show variation of velocity ( v ) with time ( t ), of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct ? 2026Consider a particle moving along a straight line, whose position as a function of time is given by s(t)= t^2- t+ , where =1 ms ⁻² , =6 ms ⁻¹ and =5 m. The average speed of the part 2026 Full Motion in One Dimension list All NEET PYQs