Answer:
vf₁ = -7.2 m/s : The first car moves in the negative x direction after the collision.
Explanation:
Theory of collisions
Linear momentum is a vector magnitude (same direction of the velocity) and its magnitude is calculated like this:
p=m*v
where
p:Linear momentum
m: mass
v:velocity
There are 3 cases of collisions : elastic, inelastic and plastic.
For the three cases the total linear momentum quantity is conserved:
P₀ = Pf Formula (1)
P₀ :Initial linear momentum quantity
Pf : Final linear momentum quantity
Data
m₁ = m kg : mass of the first car
m₂= 5m kg : mass of the second car
v₀₁ = 3.6 m/s : Initial velocity of m₁ , to the +x axis :
v₀₂= -2.4 m/s m/s : Initial velocity of m₂ , to the -x axis
vf₂= -0.24 m/s m/s : Final velocity of m₂ , to the -x axis
Problem development
We appy the formula (1):
P₀ = Pf
m₁*v₀₁ + m₂*v₀₂ = m₁*vf₁ + m₂*vf₂
We assume that the first car moves in the positive x direction after the collision., so, the sign of the final speeds is positive:
(m)*( 3.6) + (5m)*( -2.4) = (m)*vf₁ +(5m)*(- 0.24)
3.6m - 12m= m*vf₁ - 1.2m
We divided by m both sides of the equation
3.6 - 12= vf₁ -1.2
3.6 - 12 +1.2 = vf₁
-7.2 = vf₁
vf₁ = -7.2 m/s : The first car moves in the negative x direction after the collision.
