Question

A particle of mass 2kg starts moving such that its velocity V varies with distance s according to the relation V =2s⅔ when quantities are in SI unit. the work performed by the forces acting on the particle in the first 3s is​

Answer 1

Given : A particle of mass 2kg starts moving such that its velocity V varies with distance s according to the relation V =2s⅔ when quantities are in SI unit

To Find : the work performed by the forces acting on the particle in the first 3s is​

Solution:

V = 2s⅔

V = dS/dt

=> dS/dt  = 2s⅔

=> s-⅔dS  = 2dt

integrating both sides

=> 3 ∛S  = 2t + c

at t = 0   S =  0  

=> c= 0

=> 3 ∛S  = 2t

=> 27S = 8t³

=> S = 8t³/27

=> dS/dt  = 24t²/27

=> dS/dt = 8t²/9

=> v = 8t²/9

V at t = 0 is 0

V at t = 3 is 8  

Change in KE = (1/2)mv² - (1/2)mu²

(1/2) (2) (8² - 0²)

= 64 J

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