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u=1m/s
v=7m/s
distance travelled=S
v2-u2=2as
49-1=2aS
2aS=48
aS=24..................(1)
a=24/S
Distance travelled in middle of trip=12/a
Let the speed at this distance be V.
Then,
V2-u2=2aS
V2-1=2(24/S)(12/a).............(from(1))
V2=25
V=5m/s.