# Kinetic energy of an object is 25 j. Velocity is 5 m/s what will be its kinetic energy if velocity is doubles?

Feb 17, 2018

$\text{100 J}$

#### Explanation:

$\text{KE} = \left(\frac{1}{2}\right) \cdot m \cdot {v}^{2}$

Simple explanation :

Since the KE is proportional to velocity squared, if you increase the KE by a factor of $2$, you increase $v$ by a factor of ${2}^{2} = 4$

Detailed explanation :

$25 = 0.5 \cdot m \cdot \left({5}^{2}\right)$

Find $m$:

$25 = 25 \frac{m}{2}$

$m = 2$

Hence the new KE:

$\text{KE} = 0.5 \cdot 2 \cdot {10}^{2}$

$\text{KE} = 100 J$

Feb 17, 2018

The kinetic energy of body is $\text{100 J}$.

#### Explanation:

$\text{kinetic energy" =1/2 xx mxxv^2="25 J}$

$v = \text{5 m/s}$

Let the mass of body be $m$.

$\frac{1}{2} \times m \times {v}^{2} = 25$

$m \times {5}^{2} = 50$

$m \times 25 = 50$

$m = \frac{50}{25}$

or

$m = \text{2 kg}$

Now if velocity is doubled then

$v ' = 2 \cdot v$

v'=2×x5

$v ' = \text{10 m/s}$

The final kinetic energy $= \frac{1}{2} \times m \times {\left(v '\right)}^{2}$

 =1/2x×2x×10^2

 =1/2x×2x×100

$= 100 J$

Feb 17, 2018

$100 J$

#### Explanation:

We know that the equation for kinetic energy is

$K E = \frac{1}{2} m {v}^{2}$

Here, $v = 5$, $K E = 25$

$\therefore 25 = \frac{1}{2} \cdot m \cdot {5}^{2}$

$25 = \frac{1}{2} \cdot 25 \cdot m$

$\therefore m = 2$

So, the object's mass is $2 k g$.

If the velocity doubles, then $v = 5 \cdot 2 = 10$, and then

$K E = \frac{1}{2} \cdot {10}^{2} \cdot 2$

$K E = 100 J$

So, the object's kinetic energy will be $100 J$.