Question

A body is starting from rest was observed to cover 20m in particular 1s and 40mn during the next second. How far had it travelled before the first observation was taken?
(a) 2.52
(b) 2.5

Answer 1

Let x be the distance travelled before first observation is made.
u=0 m/s
V= ?
acceleration =a m/s²

By third equation of motion:
V²-u²=2as
V²-0=2ax
x=V²/2a-----(1)

Distance travelled when t= 1:
S=ut+ 1/2at²
20=Vx1+1/2a(1)²
40=2V+a------(2)

V1=V+at
=V+ax1
V1=V+a-----(3)

Distance travelled in next second:
S=ut+ 1/2at²
40=V1x1+1/2a(1)²
80=2V+2a+a
80= 2V+3a ---(equ 4)

By solving equation 2 and 4
40=2V+a
80= 2V+3a
- - -
-----------------
-40=-2a
a=20m/s²
2v =40-a
2v=40-20
2v=20
v=10m/s

now,X=V²/2a
=10*10/2*20
=10/4
=2.5m

∴ Distance travelled before the first observation was taken is 2.5m.

Hope it helps
All the best.