Question

An object starting from rest travels 20 m in first 2 s and 160 m in next 4 s. What will be the velocity after 7 s from the start?

• A. $40m{s}^{-1}$
• B. $35m{s}^{-1}$
• C. $70m{s}^{-1}$
• D. $60m{s}^{-1}$

Answer 1

The correct option is C $70m{s}^{-1}$

Displacement in first 2 s, $s_1=20m$

Displacement in first 6 s, $s_2=20+160=180m$

Note that

$s_1=5\times 2^2$

$s_2=5\times 6^2$

It can be concluded that $s=5t^2.......\left(i\right)$

$s\propto t^2⟹\text{Acceleration is constant}$

From second equation of motion for uniformly accelerated motion,

$s=ut+\left(1/2\right)a{t}^2..........\left(ii\right)$

From (i) and (ii),

$a/2=5$

$a=10m/s^2$

At the end of 7 s,

$v=u+at$

$=0+10\times 7$

$=70m/s$