Change in velocity as a vector

Steps:

• Resolve initial velocity: $\vec{v_i} = \langle 4, 0 \rangle$ m/s (right is +x).
• Resolve final velocity: $\vec{v_f} = \langle 0, -3 \rangle$ m/s (down is -y).
• Compute $\Delta \vec{v} = \vec{v_f} - \vec{v_i} = \langle -4, -3 \rangle$ m/s.
• Magnitude: $|\Delta \vec{v}| = \sqrt{(-4)^2 + (-3)^2} = \sqrt{25} = 5$ m/s.

Why B is correct:

• B shows the correct magnitude of 5 m/s, using vector subtraction and Pythagorean theorem for perpendicular components.

Why the others are wrong:

• A: Incorrectly uses scalar difference of speeds (4 - 3 = 1 m/s), ignoring direction.
• C: Adds speeds (4 + 3 = 7 m/s), violating vector principles.
• D: Matches initial speed only, not the change.

Final answer: B