Key relationship
Wnet = ΔK = ½mv² − ½mu²; Wbrake = −Fd; dstop = mu²/(2F).
Physics · Class 11
Braking and kinetic energy
The work-energy theorem connects net work to the change in kinetic energy. A brake does negative work because its force opposes displacement. The stopping distance is initial kinetic energy divided by brake force, so doubling speed quadruples stopping distance when mass and force are fixed.
Open the interactive experiment →A brake spends distance removing energy.
நிகர வேலை இயக்க ஆற்றலின் மாற்றத்திற்குச் சமம். பிரேக் எதிர்திசையில் விசை செலுத்துவதால் எதிர்மறை வேலை செய்கிறது. ஒரே விசையில் வேகம் இரட்டிப்பானால் நிறுத்தும் தூரம் நான்கு மடங்கு.
Key notes, relationships and model limits
Remember
The work-energy theorem connects net work to the change in kinetic energy. A brake does negative work because its force opposes displacement. The stopping distance is initial kinetic energy divided by brake force, so doubling speed quadruples stopping distance when mass and force are fixed.
Common trap
Continuing a constant negative acceleration past rest would reverse the cart; a real stopping brake does not do that.
Model limits
Horizontal point cart; constant opposing brake force until rest; brake disengages at rest. No other force does horizontal work.
What you will learn
Reconcile negative braking work with kinetic-energy loss and predict speed scaling.
Try the experiment
Compare original and double-speed presets. Scrub until rest and verify W = K − Kinitial.
Think of it this way
A fixed strength brake must act through more road to remove more kinetic energy.
Worked example
A 5 kg cart at 8 m/s has K = 160 J. A 10 N brake stops it in 16 m. At 16 m/s it requires 64 m.
Why this matters
The energy method can find stopping distance without first finding stopping time.
Before you start
Vector components · velocity · SI units
Check your understanding
With the same mass and braking force, doubling initial speed changes stopping distance by…
- A factor of 2
- A factor of 4
- A factor of ½
Read the explanation
Initial kinetic energy and stopping distance are proportional to the square of initial speed.
Course connection: CBSE XI Chapter 5; NEET/Main Unit 4; JEE Advanced Mechanics. Apply each exam’s stated assumptions.