An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $32 KJ$ to $96 KJ$ over $t in [0, 4 s]$ . What is the average speed of the object?

Question

An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $32 KJ$ to $96 KJ$ over $t in [0, 4 s]$ . What is the average speed of the object?

1 Answer

Impact of this question

1456 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-24T12:48:06

The average speed is $=250.2ms^-1$

Explanation:

The kinetic energy is

$KE=1/2mv^2$

mass is $=2kg$

The initial velocity is $=u_1$

$1/2m u_1^2=32000J$

The final velocity is $=u_2$

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

Therefore,

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

and,

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

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

The points are $(0,32000)$ and $(4,96000)$

The equation of the line is

$v^2-32000=(96000-32000)/4t$

$v^2=16000t+32000$

So,

$v=sqrt((16000t+32000)$

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

$(4-0)bar v=int_0^4sqrt((16000t+32000))dt$

$4 barv=[((16000t+32000)^(3/2)/(3/2*16000)]_0^4$

$=((16000*4+32000)^(3/2)/(24000))-((16000*0+32000)^(3/2)/(24000))$

$=96000^(3/2)/24000-32000^(3/2)/24000$

$=1000.8$

So,

$barv=1000.8/4=250.2ms^-1$

Science

Math

Humanities

... and beyond

An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $32 KJ$ to $96 KJ$ over $t in [0, 4 s]$ . What is the average speed of the object?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

An object has a mass of 2 kg2 kg. The object's kinetic energy uniformly changes from 32 KJ32 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:

Related questions

Impact of this question

An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $32 KJ$ to $96 KJ$ over $t in [0, 4 s]$ . What is the average speed of the object?