A body moves with a velocity of 10m/s for 10s and then with a velocity of 20m/s in the same direction for 40s. Find its initial velocity.

Dear Student,

We use the formula v=u + at
where v=final velocity
u= initial velocity
a= acceleration
t= time
Here assuming,  ${\mathrm{v}}_{1}$${\mathrm{u}}_{1}$ + a${\mathrm{t}}_{1}$   and   ${\mathrm{v}}_{2}$${\mathrm{u}}_{1}$ + a${\mathrm{t}}_{2}$
where ${\mathrm{u}}_{1}$ = initial velocity
So,

(10- ${\mathrm{u}}_{1}$)/10 = (20-${\mathrm{u}}_{1}$)/40
40 - 4${\mathrm{u}}_{1}$= 20 - ${\mathrm{u}}_{1}$
40 - 20 = 4${\mathrm{u}}_{1}$ - ${\mathrm{u}}_{1}$
20 = 3${\mathrm{u}}_{1}$
${\mathrm{u}}_{1}$= 20/3​​​​​​

So, the initial velocity = 20/3.