WHAT ARE THE FORMULAS FOR FINDING THE INITAL SPEED

I'd be happy to help you find initial speed formulas! However, I need a bit more context. Are you looking for formulas in a specific scenario? Here are the most common ones:

For motion with constant acceleration:

• v² = v₀² + 2as → v₀ = √(v² - 2as)
• v = v₀ + at → v₀ = v - at
• s = v₀t + ½at² → v₀ = (s - ½at²) / t

Where: v₀ = initial speed, v = final speed, a = acceleration, t = time, s = distance

For projectile motion:

• Horizontal component: v₀ₓ = v₀ cos(θ)
• Vertical component: v₀ᵧ = v₀ sin(θ)
• From maximum height: v₀ = √(gh × 2) where h is max height
• From range: v₀ = √(gR / sin(2θ)) where R is horizontal range

For circular motion:

• v₀ = 2πr / T where r = radius, T = period