An object has a mass of $4 kg$ . The object's kinetic energy uniformly changes from $96 KJ$ to $280 KJ$ over $t in [0, 12 s]$ . What is the average speed of the object?

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Answer 1 · 2017-02-16T12:40:25

The average speed is $=296.65ms^-1$

The initial kinetic energy is $=1/2m u^2$

So,

$1/2m u^2=96000$

$u^2=2*96000/4=48000$

$v=sqrt48000=219.1ms^-1$

The final kinetic energy is $1/2m v^2$

So,

$1/2m v^2=280000$

$v^2=2*280000/4=140000$

$v=sqrt140000=374.2ms^-1$

On a graph velocity v/s time, we have a straight line $DC$

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$AD=u$

$BC=v$

$AB=t$

Area of $ABCD=(AD+BC)/2*t$

The average speed $=barv$

$barv*t=(AD+BC)/2*t$

so,

$barv=(u+v)/2$

$=(219.1+374.2)/2$

$=296.65ms^-1$

An object has a mass of 4 kg4 kg. The object's kinetic energy uniformly changes from 96 KJ96 KJ to 280 KJ 280 KJ over t in [0, 12 s]t in [0, 12 s]. What is the average speed of the object?