Question

A body covers 12m in 2nd second and 20 m in 4th second .Find the initial velocity and acceleration of the body .

Answer 1

GIVEN :-

• A body covers 12m in 2nd second .
• A body cover 20m in 4th second .

TO FIND :-

• Initial velocity of the body (u)
• Acceleration of the body (a)

SOLUTION :-

 Formula to be used :

          $\bf S=u+a \dfrac{(2n-1)}{2}$

CASE 1

 Distance , S = 12m

 

 $\longrightarrow \sf 12 = u+a\dfrac{(2\times 2 -1)}{2}\\\\\longrightarrow 12 = u+a \times \dfrac{3}{2}\\\\\longrightarrow 2u+3a = 24 \ \ \ \ \ \ \ \ \ \ \ \ .............(1)$

CASE 2

Distance = 20m

$\longrightarrow \sf 20 = u + a \dfrac{(2\times 4-1)}{2}\\\\\longrightarrow 20 = u + a \times \dfrac{7}{2}\\\\\longrightarrow 2u+7a = 04 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

Eq (2) - Eq (1) ,

 $\hookrightarrow \sf 4a = 16\\\\\hookrightarrow \bf a = 4$

Substituting value of a in Eq (1) ,

$\hookrightarrow \sf 2u + 3 \times 4 = 24\\\\\hookrightarrow 2u + 12 = 24\\\\\hookrightarrow 2u = 12 \\\\\hookrightarrow \bf u = 6$

• Initial velocity , u = 6 m/s

• Acceleration of the body , a = 4/ms²