one dimensional motion

Question

A runner is running at 5 m/s. if during the last 100m she accelerates at 0.1 m/s what will her final velocity be?

Answer 1

v_final² = v_initial² + 2ad

v_final² = 5m/s² + 2(0.1m/s²)(100m)

v_final² = 25 + 20

v_final² = 45

Answer 2

I believe you mean that she accelerates at 0.1 m/s², not 0.1 m/s. Use the kinematic equation v² = v₀² + 2aΔx where v is the final speed, v₀ is the initial speed, a is the acceleration and Δx is the displacement:

v² = (5 m/s)² + 2(0.1 m/s²)(100 m) = 45 m²/s² ---> v = 6.7 m/s