Substitute the given velocity and mass into the formula and evaluate.
See solution.
Practice makes perfect
We are given the formula for the velocity of an object, where m is the mass and K is the kinetic energy of the object.
v=sqrt(2K/m)
In our exercise, the kinetic energy is 850 joules and the mass is 17 grams. However, the mass in this formula should be in kilograms to get the result in meters per second. Recall that one joule is 1kg* m^21s^2. Let's see why is it important by rewriting the right side of the above equation using the appropriate units.
As we can see, the mass needs to be in kilograms to get the correct velocity unit. If we keep the mass in grams, the mass unit will not reduce. Therefore, let's convert 17 grams into kilograms. Recall that one gram is 0.001 kilogram.
17 grams ⇒ 17*0.001=0.017kilograms
Now we can substitute this value for m and 850 for K in the given formula.
The velocity of the object is approximately 316.23 meters per second.
Extra
What would happen if we forgot to convert mass into kilograms first?
Let's suppose we did not remember to convert mass into kilograms before substituting it into the formula. We would substitute 17 for m and K for 850 and then evaluate.
