A particle is performing simple harmonic motion. Equation of its motion is x=5 (4 t- 6 ), x being the displacement from mean position. Velocity (in ms ⁻¹ ) of the particle at the instant when its displacement is 3 , will be

Step-by-step solution

The displacement equation is given by x = 5 (4t - 6 ) . The velocity v of a particle in simple harmonic motion is given by v = dx dt = 5 4 (4t - 6 ) = 20 (4t - 6 ) . Using the identity = 1 - ^2 , we have v = 20 1 - ^2 (4t - 6 ) . Given the displacement x = 5 (4t - 6 ) = 3 , we find (4t - 6 ) = 3 5 . Substituting this value into the velocity expression: v = 20 1 - ( 3 5 )^2 = 20 1 - 9 25 = 20 16 25 = 20 4 5 = 16 . Answer: 16