show the intermediate steps in the derivation of the impulse j or I with arrow up
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To correctly derive the impulse (J or I) with an upward arrow, you need to follow these intermediate steps:
1. Start with the definition of impulse: impulse (J or I) is equal to the change in momentum (Δp).
2. Write down the equation for momentum: momentum (p) is equal to mass (m) multiplied by velocity (v). Mathematically, p = m * v.
3. Determine the initial momentum: Determine the initial momentum of the object before the impulse is applied. Let's denote it as p₁.
4. Determine the final momentum: Determine the final momentum of the object after the impulse is applied. Let's denote it as p₂.
5. Calculate the change in momentum: The change in momentum (Δp) is equal to the final momentum (p₂) minus the initial momentum (p₁). Δp = p₂ - p₁.
6. Rewrite the equation using the upward arrow notation: Replace Δp with J or I (impulse with an upward arrow). J = p₂ - p₁.
By following these steps, you can derive the impulse (J or I) with an upward arrow notation from the definition of impulse and the equation for momentum.