A 1,450 kg car drives toward a 60 kg shopping cart that has a velocity of -1.2 m/s toward the car. The two objects collide, giving the car a final velocity of 5.13 m/s, and the shopping cart a velocity of 11.75 m/s. What was the initial velocity of the car? A. 5.67 m/s
B. 5.36 m/s
C. -5.36 m/s
D. -5.67 m/s

A) v₁ = 5.66 [m/s]

Explanation:

To solve this problem we must use the definition of linear momentum conservation, which tells us that momentum is conservation before and after a collision.

The linear momentum is equal to the mass by the product of the Velocity.

P = m*v

where:

P = lineal momentum [kg*m/s]

m = mass [kg]

v = velocity [m/s]

Now, to the right side of the equal sign will take the linear momentum before the collision and to the left side of the equal sign as after the collision.

Pbefore = Pafter

(m₁*v₁) - (m₂*v₂) = (m₁*v₃) + (m₂*v₄)

where:

m₁ = mass of the car = 1450 [kg]

v₁ = velocity of the car before the collision [m/s]

m₂ = mass of the shopping cart = 60 [kg]

v₂ = velocity of the shopping cart before the collision = -1.2 [m/s]

v₃ = velocity of the car after the collision = 5.13 [m/s]

v₄ = velocity of the shopping cart after the collision = 11.75 [m/s]

Now replacing:

(1450*v₁) - (60*1.2) = (1450*5.13) + (60*11.75)

1450*v₁ - 72 = 7438.5 + 705

1450*v₁  = 7438.5 + 705 + 72

1450*v₁ = 8215.5

v₁ = 5.66 [m/s]

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.

the right answer is 0.3 meters per second