A particle executes simple harmonic motion given by the equation x = 2 (10 t + 3 ) cm. The speed of the particle at t = 0.1 s is:

Step-by-step solution

Given equation of motion: x = 2 (10 t + 3 ) cm. The velocity of the particle is the time derivative of displacement: v = dx dt = d dt [ 2 (10 t + 3 ) ] v = 2 10 (10 t + 3 ) = 20 (10 t + 3 ) cm/s. Substituting t = 0.1 s into the velocity equation: v = 20 (10 (0.1) + 3 ) v = 20 ( + 3 ) Using the trigonometric identity ( + ) = - : v = -20 ( 3 ) = -20 1 2 = -10 cm/s. The speed is the magnitude of velocity, which is |-10 | = 10 cm/s. Answer: 10 cm/s