A ball has a mass of 4.0 kg and is moving with a velocity of 15.0 km/h. The ball increased its speed to 30.0 Km/h, then the K.E of the ball will ?

Steps please

1 Answer
Mark C.
Nov 26, 2017

OK, we need to find initial KE, final KE and the ratio between them (must be > 1) We’d normally have to start by putting velocity into SI units, but as we’re only after a ratio it won’t matter.

Explanation:

#KE_1 = 1/2m.v^2 = 1/2xx4xx15^2#

#KE_1 = 450#J

#KE_2 = 1/2m.v^2 = 1/2xx4xx30^2#

#KE _2 = 1800#J

The KE has thus gone up by a factor of #(KE_2)/(KE_1) = 1800/450# = 4.

So when velocity doubles, KE goes up by the square of that (in the equation there is a #v^2# term) and #2^2 = 4# times.

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