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

2 Answers
Jul 2, 2015

Answer:

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")#

Jul 3, 2015

Answer:

#"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.)