An object has a mass of $6 kg$ . The object's kinetic energy uniformly changes from $72 KJ$ to $120 KJ$ over $t in [0, 3 s]$ . 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 $72 KJ$ to $120 KJ$ over $t in [0, 3 s]$ . What is the average speed of the object?

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Answer 1 · 2016-03-16T07:13:22

$v_a=8/3 m/s$

Explanation:

$Delta E_k=E_"k l"-E_"k i"" " "changing of the kinetic energy of object "$
$1/2m(v_l^2-v_i^2)=120-72$
$1/2*cancel(6)(v_l^2-v_i^2)=cancel(48)$
$(v_l^2-v_i^2)=16$
$(v_l-v_i)(v_l+v_i)=16$
$v_l-v_i=2$
$v_l+v_i=8$
$2*v_l=10" "v_l=5 m/s$
$5-v_i=2$
$v_i=3 m/2$
$a=(Delta v)/(Delta t)=(v_l-v_i)/(Delta t)=(5-3)/(3-0)=1 m/s^2" (acceleration of object)"$
$v_l^2=v_i^2+2*a*Delta x$
$5^2=3^2+2*1*Delta x$
$25=9+2*Delta x$
$16=2*Delta x$
$Delta x=8 m" displacement for (0-3)"$
$"Average velocity of an object is given by:"$
$v_a=("Total displacement")/("Total time")$
$v_a=8/3 m/s$

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An object has a mass of $6 kg$ . The object's kinetic energy uniformly changes from $72 KJ$ to $120 KJ$ over $t in [0, 3 s]$ . 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 72 KJ72 KJ to 120 KJ 120 KJ over t in [0, 3 s]t in [0, 3 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 $72 KJ$ to $120 KJ$ over $t in [0, 3 s]$ . What is the average speed of the object?