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,
$\frac{{\mathrm{v}}_{1 }- {\mathrm{u}}_1}{{\mathrm{t}}_1}=\mathrm{a}=\frac{{\displaystyle {\mathrm{v}}_2 - {\mathrm{u}}_1}}{{\mathrm{t}}_2}$
(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.
Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards