SOLUTION: Can someone please help me with this problem: The speed of a 4000-kg truch whose KE is 1.8 MJ is: a. 0.95 m/s b. 30 m/s c. 94 m/s d. 900 m/s

Algebra ->  Length-and-distance -> SOLUTION: Can someone please help me with this problem: The speed of a 4000-kg truch whose KE is 1.8 MJ is: a. 0.95 m/s b. 30 m/s c. 94 m/s d. 900 m/s      Log On


   

Question 190776: Can someone please help me with this problem:
The speed of a 4000-kg truch whose KE is 1.8 MJ is:
a. 0.95 m/s
b. 30 m/s
c. 94 m/s
d. 900 m/s
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you've been given the kinetic energy formula: KE=%281%2F2%29mv%5E2 where "KE" is the kinetic energy (think of it as the energy it has when it is moving), "m" is the mass, and "v" is the velocity


Note: the units for the three variables are:

KE: joules (j)
m: kilograms (kg)
v: meters per second (m/s)

the units in this problem are very important


First, take note that 4000 kg in scientific notation is written as m=4%2A10%5E3 kilograms


Also, 1.8 MJ (1.8 megajoules) can be written as 1,800,000 joules, which is 1.8%2A10%5E6 joules. So the kinetic energy is KE=1.8%2A10%5E6 joules.



KE=%281%2F2%29mv%5E2 Start with the given formula


1.8%2A10%5E6=%281%2F2%29%284%2A10%5E3%29v%5E2 Plug in KE=1.8%2A10%5E6 and m=4%2A10%5E3


1.8%2A10%5E6=%282%2A10%5E3%29v%5E2 Multiply 1%2F2 by 4%2A10%5E3 to get 2%2A10%5E3


%281.8%2A10%5E6%29%2F%282%2A10%5E3%29=v%5E2 Divide both sides by 2%2A10%5E3.


900=v%5E2 Divide


v%5E2=900 Rearrange the equation


v=sqrt%28900%29 Take the square root of both sides (we're only interested in the positive square root)


v=30 Take the square root of 900 to get 30


So the velocity is 30 m/s