Question

the the objects below from greatest to least (greatest at the top)
possible points 1.03
m = 1 kg & v = 5 m/s
m = 5 kg & v = 2 m/s
m = 5 kg & v = 4 m/s
m = 10 kg & v = 2 m/s

Explanation:

Step1: Calculate kinetic energy for each object

The formula for kinetic energy \(K.E.=\frac{1}{2}mv^{2}\)
For \(m = 1\space kg\) and \(v=5\space m/s\):
\(K.E._{1}=\frac{1}{2}\times1\times5^{2}=\frac{25}{2}=12.5\space J\)
For \(m = 5\space kg\) and \(v = 2\space m/s\):
\(K.E._{2}=\frac{1}{2}\times5\times2^{2}=\frac{1}{2}\times5\times4 = 10\space J\)
For \(m = 5\space kg\) and \(v = 4\space m/s\):
\(K.E._{3}=\frac{1}{2}\times5\times4^{2}=\frac{1}{2}\times5\times16=40\space J\)
For \(m = 10\space kg\) and \(v = 2\space m/s\):
\(K.E._{4}=\frac{1}{2}\times10\times2^{2}=\frac{1}{2}\times10\times4 = 20\space J\)

Step2: Compare the kinetic energies

We have \(K.E._{3}=40\space J\), \(K.E._{4}=20\space J\), \(K.E._{1}=12.5\space J\), \(K.E._{2}=10\space J\)

Answer:

\(m = 5\space kg\space \&\space v = 4\space m/s\) (top), \(m = 10\space kg\space \&\space v = 2\space m/s\), \(m = 1\space kg\space \&\space v = 5\space m/s\), \(m = 5\space kg\space \&\space v = 2\space m/s\) (bottom)