The first car has twice the mass of a second car, but only half as much kinetic energy. when both cars increase their speed by 9.0 m/s, they then have the same kinetic energy. what were the original speeds of the two cars? express your answers using two significant figures separated by a comma?

Speed of the car 1 =

Speed of the car 2 =

Explanation:

Given:

Mass of the car 1 , M₁ = Twice the mass of car 2(M₂)

mathematically,

M₁ = 2M₂

Kinetic Energy of the car 1 = Half the kinetic energy of the car 2

KE₁ = 0.5 KE₂

Now, the kinetic energy for a body is given as

where,

m = mass of the body

v = velocity of the body

thus,

or

or

or

or

or

 .................(1)

also,

or

or

or

or

or

or

or

or

and, from equation (1)

Hence,

Speed of car 1 =

Speed of car 2 =

The original speeds of the two cars were :

Explanation:

Let's start reading the question and making our equations in order to find the speeds.

The first equation is :

(I)

The kinectic energy can be calculated using the following equation :

(II)

Where ''K'' is the kinetic energy

Where ''m'' is the mass and where ''v'' is the speed.

By reading the exercise we find that :  

(III)

If we use (II) in (III) :

(IV)

If we replace (I) in (IV) ⇒

(V)

'' When both cars increase their speed by , they then have the same kinetic energy ''

The last equation is :

(VI)

If we use (I) in (VI) ⇒

If we use (V) in this last expression ⇒

We find that the original speed is

If we replace this value in the equation (V) ⇒

your answer is c! hope this : )