When solving kinetic energy problems, you may be asked to find 3 variables. These variables are the kinetic energy, the mass, or the speed.

**Problem # 1:**

Suppose a car has 3000 Joules of kinetic energy. What will be its kinetic energy if the speed is doubled? What if the speed is tripled?

**Solution:**

We already proved in kinetic energy lesson that whenever the speed is doubled, the kinetic energy is quadrupled or four times as big.

4 × 3000 = 12000

Therefore, the kinetic energy is going to be 12000 joules.

Let v be the speed of a moving object. Let speed = 3v after the speed is tripled.

K = m

(3v)^{2}
2

K = m

9v^{2}
2

K = 9

mv^{2}
2

The 9 that you see means that the kinetic energy is multiplied by 9.

9 × 3000 = 27000

Therefore, the kinetic energy is going to be 27000 joules.

**Problem # 2:**

Calculate the kinetic energy of a 10 kg object moving with a speed of 5 m/s. Calculate the kinetic energy again when the speed is doubled.

**Solution:**

K = m

v^{2}
2

K = 10

5^{2}
2

K =
^{2}

10
2

× 5K = 5 × 5

K = 5 × 25 = 125 joules

Now, calculate again whe the speed is doubled.

K = m

v^{2}
2

K = 10

10^{2}
2

K =
^{2}

10
2

× 10K = 5 × 10

K = 5 × 100 = 500 joules

As you can see, the kinetic energy is quadrupled since 4 × 125 = 500

**Problem # 3: **

Suppose a rat and a rhino are running with the same kinetic energy. Which one do you think is going faster?

**Solution:**

The only tricky and hard part is to use the kinetic energy formula to solve for v.

K =
^{2}

1
2

mvMultiply both sides by 2

2 × K = 2 ×
^{2}

1
2

mv
2 × K =
^{2}

2
2

mv2K = mv

Divide both sides by m

2K
m

= vSince the kinetic energy is the same, 2 × K is the same for the rat and the rhino.

When the numerator of two fractions is the same, the bigger fraction is the one with the smaller denominator.

Since the rat has a smaller mass, then

2K
m

will be bigger for the rat
This result also means that v

**Problem # 4: **

The kinetic energy of an object is 8 times bigger than the mass. Is it possible to get speed of the object?

Think carefully and try to solve this problem yourself.

If you still cannot do it, click here to see the solution.
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