An object has a mass of $6 kg$ . The object's kinetic energy uniformly changes from $96 KJ$ to $108 KJ$ over $t in [0, 6 s]$ . What is the average speed of the object?

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An object has a mass of $6 kg$ . The object's kinetic energy uniformly changes from $96 KJ$ to $108 KJ$ over $t in [0, 6 s]$ . What is the average speed of the object?

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Answer 1 · 2017-03-17T09:11:50

The average speed is $=184.4ms^-1$

Explanation:

The kinetic energy is

$KE=1/2mv^2$

The initial velocity is $=u_1$

$1/2m u_1^2=96000J$

The final velocity is $=u_2$

$1/2m u_2^2=108000J$

Therefore,

$u_1^2=2/6*96000=32000m^2s^-2$

and,

$u_2^2=2/6*108000=36000m^2s^-2$

The graph of $v^2=f(t)$ is a straight line

The points are $(0,32000)$ and $(6,36000)$

The equation of the line is

$v^2-32000=(36000-32000)/6t$

$v^2=666.7t+32000$

So,

$v=sqrt((666.7t+32000)$

We need to calculate the average value of $v$ over $t in [0,6]$

$(6-0)bar v=int_0^6sqrt((666.7t+32000)dt$

$6 barv=[((666.7t+32000)^(3/2)/(3/2*666.7)]_0^6$

$=((666.7*6+32000)^(3/2)/(1000))-((666.7*0+32000)^(3/2)/(1000))$

$=36000^(3/2)/1000-32000^(3/2)/1000$

$=1106.2$

So,

$barv=1106.2/6=184.4ms^-1$

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An object has a mass of $6 kg$ . The object's kinetic energy uniformly changes from $96 KJ$ to $108 KJ$ over $t in [0, 6 s]$ . What is the average speed of the object?

1 Answer

Explanation:

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An object has a mass of 6 kg6 kg. The object's kinetic energy uniformly changes from 96 KJ96 KJ to 108 KJ 108 KJ over t in [0, 6 s]t in [0, 6 s]. What is the average speed of the object?

1 Answer

Explanation:

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An object has a mass of $6 kg$ . The object's kinetic energy uniformly changes from $96 KJ$ to $108 KJ$ over $t in [0, 6 s]$ . What is the average speed of the object?