#### 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.

We can observe that the distance travelled in consecutive seconds is increasing hence we can conclude that object is accelerating.

Let its initial speed is u and acceleration is a.

Hence, by the 2nd equation of motion we can write:

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

$20= u(2) + \frac{1}{2}a(2)^{2}$

$\Rightarrow 20= 2u +2a$

$\Rightarrow 10= u +a$ ..................(i)

and

$180 =u (6)+ \frac{1}{2}a(6)^{2}$

$180 =6u+ 18 a$

$\Rightarrow 30 =u+ 3 a$  ............(ii)

Solving (i) and (ii)

u = 0

$a= 10m /s^{2}$

Since, acceleration is same, the velocity after 7 s from the start will be $v' = 0+(10\times 7 ) = 70 \;ms^{-1}$