Concept:Use Newton's second law and kinematics to find the final velocity, then apply the work-energy theorem or calculate kinetic energy differences.
Formula:$$ p = mv \quad ; \quad a = \frac{F}{m} \quad ; \quad v_f = v_i + at \quad ; \quad \Delta K.E = \frac{1}{2}m(v_f^2 - v_i^2) $$
Solution:- Find initial velocity: \( 10 = 5 \times v_i \Rightarrow v_i = 2 \text{ m/s} \).
- Find acceleration: \( a = \frac{0.2}{5} = 0.04 \text{ m/s}^2 \).
- Find final velocity after 10s: \( v_f = 2 + (0.04 \times 10) = 2 + 0.4 = 2.4 \text{ m/s} \).
- Calculate K.E difference: \( \Delta K.E = \frac{1}{2}(5)(2.4^2 - 2^2) \).
- \( \Delta K.E = 2.5(5.76 - 4) = 2.5(1.76) \).
- \( 2.5 \times 1.76 = 4.4 \text{ J} \).
Why other options are incorrect:Mistakes in calculating \( 2.4^2 \) or mistakenly doing \( (v_f - v_i)^2 \) lead to incorrect values like 0.4 J or other distractors.
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