An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $16 KJ$ to $96 KJ$ over $t in [0, 4 s]$ . 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 $16 KJ$ to $96 KJ$ over $t in [0, 4 s]$ . What is the average speed of the object?

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Answer 1 · 2017-04-28T06:21:39

The average speed is $=231ms^-1$

Explanation:

The kinetic energy is

$KE=1/2mv^2$

mass is $=2kg$

The initial velocity is $=u_1$

$1/2m u_1^2=16000J$

The final velocity is $=u_2$

$1/2m u_2^2=96000J$

Therefore,

$u_1^2=2/2*16000=16000m^2s^-2$

and,

$u_2^2=2/2*96000=96000m^2s^-2$

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

The points are $(0,16000)$ and $(4,96000)$

The equation of the line is

$v^2-16000=(96000-16000)/4t$

$v^2=20000t+16000$

So,

$v=sqrt((20000t+16000)$

We need to calculate the average value of $v$ over $t in [0,4]$

$(4-0)bar v=int_0^4sqrt((20000t+16000))dt$

$4 barv=[((20000t+16000)^(3/2)/(3/2*20000)]_0^4$

$=((20000*4+16000)^(3/2)/(30000))-((20000*0+16000)^(3/2)/(30000))$

$=96000^(3/2)/30000-16000^(3/2)/30000$

$=924$

So,

$barv=924/4=231ms^-1$

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An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $16 KJ$ to $96 KJ$ over $t in [0, 4 s]$ . What is the average speed of the object?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

An object has a mass of 2 kg2 kg. The object's kinetic energy uniformly changes from 16 KJ16 KJ to 96 KJ96 KJ over t in [0, 4 s]t in [0, 4 s]. 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 $16 KJ$ to $96 KJ$ over $t in [0, 4 s]$ . What is the average speed of the object?