Question

A point moves in a straight line so that its displacement x at time t is given by
x^2=1+t^2 .It's acceleration at any time t is ??

Answer 1

Answer:

x2=t2+1

taking its differentiation,

2x*(dx/dt)=2t

x*(dx/dt)=t

again taking differentiation for acceleration,

x*(d2x/dt2) + (dx/dt)2 = 1

x*(d2x/dt2) = 1 – (dx/dt)2

x*(d2x/dt2) = 1 – (t/x)2                  (because x*(dx/dt)=t)

(d2x/dt2) = (1 – (t/x)2)/x

(d2x/dt2) = 1/x – t2/x3

put t2 = x2 -1

(d2x/dt2) = 1/x3