A body of mass m starts moving from rest along x - axis so that its velocity varies as v = a s where a is a…

A body of mass m starts moving from rest along x-axis so that its velocity varies as v=as where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t second after the start of the motion is
  1. 8 ma4t2
  2. 14 ma4t2 
  3. 4 ma4t2
  4. 18ma4t2

Solution

v=as=dsdt

⇒dss=a.dt

⇒2s=at

⇒s=a2t24, v=dsdt=a2t2

⇒Wall=∆K=Kf-Ki

⇒Wall=12mv22-v12

⇒v1=0, v2=a2t2

⇒Wall=12ma2t22-0

⇒Wall=18ma4t2

⇒Wall=∆K

Asked in: JEE Main 2018 (16 Apr Online)

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