A 3 kg exercise ball rolls across a gym floor carrying 54 J of kinetic energy.
No speed in sight. The lesson unwraps the measured joules to get it back.
Work the numbers first. Double the ball's 54 J: 54 × 2 = 108.
Divide by the 3 kg mass: 108 ÷ 3 = 36. That is the speed squared: v² = 36.
Find the number that multiplies by itself to give 36: 6 × 6 = 36, so v = 6. The ball rolls at 6 m/s.
Now the equation behind the moves. Doubling cleared the half, and dividing removed the mass: v² = 2 × KE ÷ m, then v is the square root.
The mass unwraps with no square root: m = 2 × KE ÷ v².
A 4 kg sled carries 200 J of kinetic energy. Calculate its speed.
Write down the values:
KE = 200 J, m = 4 kg, v = ?
Write down the equation:
v² = 2 × KE ÷ m
Double the energy: 200 × 2 = 400.
Substitute in the values, and calculate:
v² = 400 ÷ 4 = 100
v² = 100, and 10 × 10 = 100, so the sled's speed is 10 m/s.
A cart moving at 5 m/s carries 150 J of kinetic energy. Calculate its mass.
Write down the values:
KE = 150 J, v = 5 m/s, m = ?
Write down the equation:
m = 2 × KE ÷ v²
Double the energy: 150 × 2 = 300. The speed squared: 5 × 5 = 25.
Substitute in the values, and calculate:
m = 300 ÷ 25 = 12
The cart's mass is 12 kg.
Talia knows a wagon's kinetic energy and its mass. Which expression gives the speed squared?
The same wagon: its kinetic energy is 160 J and its mass is 5 kg. Enter its speed in m/s.
A curling stone glides at 2 m/s carrying 38 J of kinetic energy. Enter its mass in kg.
A 10 kg toolbox slides off a loading ramp carrying 245 J of kinetic energy. Enter its speed in m/s.
A loaded wheelbarrow moving at 6 m/s carries 234 J of kinetic energy. Enter its mass in kg.
Four vehicles approach a toll plaza. To compare them, calculate each kinetic energy. Which vehicle has the greatest kinetic energy?