This key facts covers How to Rearrange the KE Equation within Kinetic Energy for GCSE Physics. Revise Kinetic Energy in Energy for GCSE Physics with 15 exam-style questions and 30 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 15 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
🔧 How to Rearrange the KE Equation
Starting equation: Ek = ½mv²
To find mass (m):
- Multiply both sides by 2: 2Ek = mv²
- Divide by v²: m = 2Ek / v²
To find velocity (v):
- Multiply both sides by 2: 2Ek = mv²
- Divide by m: 2Ek/m = v²
- Square root both sides: v = √(2Ek/m)
💡 Exam tip: When finding v, you MUST square root at the end. Many students forget this step and lose marks!
Worked method: using the rearranged KE equation
The page gives you the three forms — this is how to use them under exam conditions.
- Pick the form BEFORE you substituteDecide which quantity is missing first, then choose the matching form. Substituting into Ek = ½mv² and rearranging afterwards with numbers already in is where most arithmetic slips happen.
- Watch the units going inMass must be in kilograms and velocity in metres per second, or the answer is wrong even with perfect algebra. A mass given in grams must be divided by 1000 first; a speed in km/h must be divided by 3.6.
- Square root LAST when finding velocityWork out 2Ek ÷ m completely, then take the square root of that single number. Taking the root of 2Ek before dividing by m is the most common route to a wrong answer.
- Sense-check the size of your answerA car is a few tens of m/s, not hundreds. If velocity comes out implausibly large, you have probably forgotten to square-root, or divided by v instead of v².
A 1200 kg car has 240 000 J of kinetic energy. Calculate its speed.
v = √(2Ek ÷ m) = √(2 × 240000 ÷ 1200) = √(480000 ÷ 1200) = √400 = 20 m/s
The most commonly lost mark is taking the square root too early, or squaring the mass instead of the velocity. Divide fully first, then root the single number that remains.
Practice questions for Kinetic Energy
Which of the following objects has kinetic energy stored in its kinetic energy store?
A car travels at 20 m/s. The driver then doubles their speed to 40 m/s. Explain what happens to the kinetic energy of the car and by what factor it changes.