An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $18 KJ$ to $54KJ$ over $t in [0,12s]$ . 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 $18 KJ$ to $54KJ$ over $t in [0,12s]$ . What is the average speed of the object?

1 Answer

Impact of this question

1452 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-14T06:56:51

The average speed is $=187.7ms^-1$

Explanation:

The kinetic energy is

$KE=1/2mv^2$

mass is $=2kg$

The initial velocity is $=u_1$

$1/2m u_1^2=18000J$

The final velocity is $=u_2$

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

Therefore,

$u_1^2=2/2*18000=18000m^2s^-2$

and,

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

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

The points are $(0,18000)$ and $(12,54000)$

The equation of the line is

$v^2-18000=(54000-18000)/12t$

$v^2=3000t+18000$

So,

$v=sqrt((3000t+18000)$

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

$(12-0)bar v=int_0^12sqrt((3000t+18000))dt$

$12 barv=[((3000t+18000)^(3/2)/(3/2*3000)]_0^12$

$=((3000*12+18000)^(3/2)/(4500))-((3000*0+18000)^(3/2)/(4500))$

$=54000^(3/2)/4500-18000^(3/2)/4500$

$=2251.9$

So,

$barv=2251.9/12=187.7ms^-1$

Science

Math

Humanities

... and beyond

An object has a mass of $2 kg$ . The object's kinetic energy uniformly changes from $18 KJ$ to $54KJ$ over $t in [0,12s]$ . 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 18 KJ18 KJ to 54KJ 54KJ over t in [0,12s]t in [0,12s]. 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 $18 KJ$ to $54KJ$ over $t in [0,12s]$ . What is the average speed of the object?