Question

What is the kinetic energy of an object with a mass of `6.25xx10^4` `"g"` having a speed of `"26.3 m/s"`?

Answer 1

The person's kinetic energy is equal to 21.6 kJ.

Explanation:

Kinetic energy is simply a measure of how much work needs to be done in order to accelerate an object from complete rest to a given velocity.

Mathematically, kinetic energy is defined as

`K_E = 1/2 * m* v^2`, where

`m` - the mass of the object - expressed in kilograms;
`v` - the velocity of the object - expressed in meters per second.

So, convert the mass of the person from grams to kilograms

`6.25 * 10^4cancel("g") * "1 kg"/(10^3cancel("g")) = "62.5 kg"`

Now plug your values into the equation and solve for `K_E`

`K_E = 1/2 * "62.5 kg" * 26.2""^2 "m"^2/"s"^2`

`K_E = 1/2 * 62.5 * 26.2""^2 * underbrace(("kg" * "m"^2)/"s"^2)_(color(blue)("=Joule"))`

`K_E = "21615. 3 J"`

Rounded to three sig figs and expressed in kilojoules, the answer will be

`K_E = 21615.3cancel("J") * "1 kJ"/(1000cancel("J")) = color(green)("21.6 kJ")`

Answer 2

`"21600 J"` (Rounded to three significant figures.)

Explanation:

`"KE"=1/2*m*v^2`, where KE is kinetic energy in Joules, `m` is mass in kilograms, and `v^2` is speed in m/s squared.

Known

mass = `(6.25xx10^4cancel"g")xx(1"kg")/(1000cancel"g")="62.5 kg"`
speed = `"26.3 m/s"`

Unknown
Kinetic energy

Solution
`"KE"=1/2*m*v^2`

`"KE"=1/2*62.5"kg"*(26.3"m/s")^2`

`"KE"` `=21600 "kg·m"^2"/s"^2"`=`21600 "J"`
(Rounded to three significant figures.)