The Kinetic Energy K, in Joules, Provided by the Mass of a Particle m GMAT Problem Solving

Question: The kinetic energy K, in joules, provided by the mass of a particle m, in kilograms, with a velocity of v meters per seconds, is given by the equation K = 12 mv2. If a particle had a velocity of 4 meters per second and a kinetic energy of 144 joules, then the mass, in kilograms, of this particle must be

1. 16
2. 18
3. 24
4. 44
5. 64

“The Kinetic Energy K, in Joules, Provided by the Mass of a Particle m GMAT Problem Solving” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical understanding.

Solution and Explanation:

Approach Solution 1: 

The given situation states that The kinetic energy K, in joules, provided by the mass of a particle m, in kilograms, with a velocity of v meters per seconds, is given by the equation K = \(\frac{1}{2}mv^2\).
To find the mass, in kilograms, of this particle lets solve this question using basic arithmetic
We know that
K = \(\frac{1}{2}mv^2\).
Lets solve it further by putting the values in equation
144 = \(\frac{1}{2}m*4^2\).
144 = \(\frac{1}{2}m*16\)
288 = 16m
m = \(\frac{288}{16}\)
m= 18
The mass of the particle is 18kg

Correct Answer: B

Approach Solution 2: 

Explanation- we are given that The kinetic energy K, in joules, provided by the mass of a particle m, in kilograms, with a velocity of v meters per seconds, is given by the equation K = \(\frac{1}{2}mv^2\). to find the mass If a particle had a velocity of 4 meters per second and a kinetic energy of 144 joules we need to use the following approach
We know that , K = \(\frac{1}{2}mv^2\)
so,
144 = \(\frac{1}{2}mv^2\)
144 =\(\frac{1}{2}m*4^2\)
144 = \(\frac{1}{2}m*16\)
144 = 8m
m = \(​​​​\frac{144}{8}\)
m= 18
The mass of the particle is 18kg

Correct Answer: B

Approach Solution 3: 

Following the formula of kinetic energy, we get the equation:

144 = 1/2*m*16

solving the equation, we get, 8m = 144

Therefore, m = 144/8 = 18.

Hence, the mass, in kilograms, of this particle must be 18kg.

Correct Answer: B

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