Question

A body travels 10m in 5th second and 30m in 10th second. Find its initial velocity and acceleration.

Answer 1

assuming constant acceleration from position s(0)=0,

s(t) = vt + 1/2 at^2

So, we have

s(5)-s(4) = 10
s(10)-s(9) = 30

now just plug in the numbers and you get

5v+25(a/2)-(4v+16(a/2)) = 10
10v+100(a/2)-(9v+81(a/2)) = 30

Now just solve for a and v.