Question:
An object starting from rest travels $20 \mathrm{~m}$ in first $2 \mathrm{~s}$ and $160 \mathrm{~m}$ in next $4 \mathrm{~s}$. What will be the velocity after $7 \mathrm{~s}$ from the start?
Solution:
Ist Case :
Here $u=0, \mathrm{~S}_{1}=20 \mathrm{~m}, t_{1}=2 \mathrm{~s}$
Using $S_{1}=u t_{1}+\frac{1}{2} a t_{1}^{2}$, we get
$20=0+\frac{1}{2} a \times 4=2 a$
or $a=10 \mathrm{~ms}^{-2}$
2nd Case :
$\mathrm{S}_{2}=160 \mathrm{~m}, t_{2}=4 \mathrm{~s}$
$\therefore S_{1}+S_{2}=20+160=180 \mathrm{~m}$
$t_{1}+t_{2}=2+4=6 \mathrm{~s}$
$\therefore 180=\frac{1}{2} a \times 36=18 a$
or $a=10 \mathrm{~ms}^{-2}$
Velocity after $7 \mathrm{~s}, v=u+a t=0+10 \times 7=70 \mathrm{~ms}^{-1}$