Question

A particle moving with a uniform acceleration along a straight line covers distances a and b in successive intervals of p and q second. The acceleration of the particle is

Answer 1

a particle moving with uniform acceleration along straight line covers distances a and b in successive intervals of p and q second . the acceleration of the particle is

Answer 2

Answer:

   The correct answer is $\frac{2(pb-aq)}{pq(p+q)}$ .

Explanation:

   According to the given problem, when

               $s=a , t=p$

      We know that

                 $s=ut+\frac{1}{2}ct^{2}$     (Where c = accleration)

       (or)    $a=up+\frac{1}{2}cp^{2}$

                    $a=up+\frac{cp^{2}}{2}$       equation 1

     For $s=p, t=q$ then

                    $b=u(p+q)+\frac{c(p+q)^{2} }{2} -up-\frac{1}{2}c(p+q)^{2}$

                       $=uq+\frac{1}{2} c(q^{2} +2pq)aq-bp$

                       $=\frac{1}{2}c^{2} q-\frac{1}{2}cp(q^{2} +2pq)$

                   $c=\frac{2(pb-aq)}{pq(p+q)}$