Question

A body covers 100cm in the first 2s and 128 cm in the next 4s moving with constant acceleration. The velocity of the body at the end of 8s is

• A. $10c{m}^{-1}$
• B. $9c{m}^{-1}$
• C. $8c{m}^{-1}$
• D. $6c{m}^{-1}$

Answer 1

The correct option is C $8c{m}^{-1}$

Find the $V=?$

Consider initial velocity of object be ${}^{\prime }{u}^{\prime }$ and acceleration be ${}^{\prime }{a}^{\prime }$ from 2nd kinematical equation of motion we have,

$x=ut+\frac{1}{2}{at}^2$

From given information we have two equation :-

$2u+2a=100$ (for, $t=2s$ and $x=100cm$)

$6u+18a=228$ (for $x=100+128=228$)

$t=2+4=6s$

On solving these equations we get $u=56cm/s$

and $a=-6cm/s^2$ and by using $v=u+at$

Velocity at the end of $8s$ is -

$V=56-1\times 8=56-48=+8cm/s$.