A 10 kg block rests on horizontal surface with μₛ=μₖ=0.50 and g=10 m/s². Force F increases linearly from 0 to 100 N over t=0–4 s (graph), then becomes 40 N. Find speed at t=4 s (m/s).
Physics · Mixed Chapter
JEE Main Practice

Question

A 10 kg block rests on horizontal surface with μₛ=μₖ=0.50 and g=10 m/s². Force F increases linearly from 0 to 100 N over t=0–4 s (graph), then becomes 40 N. Find speed at t=4 s (m/s).

G1 Physics · Accepted Answer

Step 1: Limiting friction f=μmg=0.5×10×10=50 N. Step 2: During 0≤t≤4, F(t)=25t N; movement begins when F=50⇒t=2 s. Step 3: During 2–4 s, net force F−50=25t−50 N. Step 4: Δv=(1/10)∫₂⁴(25t−50)dt=(1/10)[12.5t²−50t]₂⁴=5 m/s.