An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $48 KJ$ to $54KJ$ over $t in [0,12s]$ . What is the average speed of the object?

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An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $48 KJ$ to $54KJ$ over $t in [0,12s]$ . What is the average speed of the object?

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Answer 1 · 2017-05-06T10:08:26

The average speed is $=159.7ms^-1$

Explanation:

The kinetic energy is

$KE=1/2mv^2$

mass is $=2kg$

The initial velocity is $=u_1$

$1/2m u_1^2=48000J$

The final velocity is $=u_2$

$1/2m u_2^2=54000J$

Therefore,

$u_1^2=2/4*48000=24000m^2s^-2$

and,

$u_2^2=2/4*54000=27000m^2s^-2$

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

The points are $(0,24000)$ and $(12,27000)$

The equation of the line is

$v^2-24000=(27000-24000)/12t$

$v^2=250t+24000$

So,

$v=sqrt((250t+24000)$

We need to calculate the average value of $v$ over $t in [0,12]$

$(12-0)bar v=int_0^12sqrt((250t+24000))dt$

$12 barv=[((250t+24000)^(3/2)/(3/2*250)]_0^12$

$=((250*12+24000)^(3/2)/(375))-((250*0+24000)^(3/2)/(375))$

$=27000^(3/2)/375-24000^(3/2)/375$

$=1916$

So,

$barv=1916/12=159.7ms^-1$

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An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $48 KJ$ to $54KJ$ over $t in [0,12s]$ . What is the average speed of the object?

1 Answer

Explanation:

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An object has a mass of 2 kg2 kg. The object's kinetic energy uniformly changes from 48 KJ48 KJ to 54KJ 54KJ over t in [0,12s]t in [0,12s]. What is the average speed of the object?

1 Answer

Explanation:

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An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $48 KJ$ to $54KJ$ over $t in [0,12s]$ . What is the average speed of the object?