Q) Let d(t) be
the position of an object at time t, and let r(t) be its velocity (r=d”)....

Question

Q) Let d(t) be
the position of an object at time t, and let r(t) be its velocity (r=d”). Use
implicit differentiation to show that the formula d=rt is
valid only when the object is moving with constant velocity.Bottom of Form

Robert · Accepted Answer

given 
        displacement of object = d(t)
        velocity of object = r(t) 
To Prove :    d = r*t ; only if velocity is constant .  
 d(t) = r(t) * t ;
by chain rule of differentiation
   d(d(t))/dt = d(r(t))/dt * t + r(t) * d(t)/dt
  
  if velocity is constant  d(r(t))/dt = 0 ;

Q) Let d(t) be the position of an object at time t, and let r(t) be its velocity (r=d”). Use implicit differentiation to show that the formula d=rt is valid only when the object is moving with...

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