A sports car of mass m has the same kinetic energy as an SUV with a mass 3m as each is driven along the same road. Which vehicle, if either, has the larger momentum and what is the difference in their momenta, if any

Explanation:

Kinetic energy ( KE ) = 1/2 m v²

= m²v² / 2 m = p² / 2m where p is momentum

KE = p² / 2m

p² = 2m KE

KE is constant

p is proportional to mass

So car having higher mass will have higher momentum .

p₁ = √ ( 2 m x KE )

p₂ = √ ( 6 m x KE )

p₂ - p₁ =  √ ( 6 m x KE ) - √ ( 2 m x KE )

= √KE m ( √6 - √2 )

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