The ball’s initial speed was 4.15 m/s.

How to see this with kinematics

We know:

  • Acceleration a=−0.100a=-0.100a=−0.100 m/s² (negative because it is opposite the velocity).
  • Final speed v=4.00v=4.00v=4.00 m/s.
  • Displacement x=6.00x=6.00x=6.00 m.

Use the kinematic relation:

v2=v02+2axv^2=v_0^2+2axv2=v02​+2ax

where v0v_0v0​ is the initial speed. Plug in the numbers:

(4.00)2=v02+2(−0.100)(6.00)(4.00)^2=v_0^2+2(-0.100)(6.00)(4.00)2=v02​+2(−0.100)(6.00)

16.0=v02−1.2016.0=v_0^2-1.2016.0=v02​−1.20

v02=17.2v_0^2=17.2v02​=17.2

v0=17.2≈4.15textm/sv_0=\sqrt{17.2}\approx 4.15\\text{m/s}v0​=17.2​≈4.15textm/s

So the ball started slightly faster (4.15 m/s) and slowed down to 4.00 m/s over 6.00 m due to the small opposing acceleration.

TL;DR: Initial speed ≈ 4.15 m/s.

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