Question

The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared, given by a = α v2 , where v > 0 m/s and α = −1.68 m−1 . If the marble enters this fluid with a speed of 2.24 m/s, how long will it take before the marble’s speed is reduced to half of its initial value? Answer in units of s.

Answer 1

t = 0.133 s

Step-by-step explanation:

given,

a = α v²

α = −1.68 m⁻¹

speed of the marble entering, v_i = 2.24 m/s

final marble speed
`v_f = (v_i)/(2)`

Acceleration of marble fluid

a = -1.68 v²

v = 2.24 m/s

a = -1.68 x 2.24² = -8.43 m/s²

using equation of motion

v = u + a t

2.24/2 = 2.24 - 8.43 x t

8.43 t = 1.12

t = 0.133 s

hence, time taken by the stone to decelerate to half velocity is equal to 0.133 s.