Answer:
a) The kinetic energy of the two cars is the same
the moment of car 2 is greater than the moment of car 1
b) the kinetic energy of car 1 is greater than that of car 2
the moment of the two cars is the same
Step-by-step explanation:
a) to know the kinetic energy of each car, we must find the speed, use Newton's second law to find the acceleration
Car 1
F = m a
a = F / m
Let's use kinematics to find the velocity after x = 1 m
v² = v₀² + 2 a x
The initial speed is zero
v = √ (2 F/m x)
For the distance of x = 1 m
v₁ = √ (2 F / m)
Car 2
F = 2m a
a = F / 2m
v² = 2 a x
v = √ (F/m x)
For x = 1 m
v₂ = √(F / m)
Let's calculate the kinetic energy of each car
Car 1
K₁ = ½ m v₁²
K₁ = ½ m 2F / m
K₁ = F
Car 2
K₂ = ½ 2m v₂²
K₂ = ½ 2m F / m
K₂ = F
The kinetic energy of the two cars is the same
Let's calculate the moment
Car 1
P₁ = m v₁
P₁ = m √ (2F / m)
Car 2
P₂ = 2m v²
P₂ = 2m √(F / m)
We see that the moment of car 2 is greater than the moment of car 1
b) in this part the force is applied by t = 10 s
Acceleration is the same, let's find the speed
Car1
v = v₀ + a t
v = F / m t
v₁ = F / m 10
Car 2
v₂ = F / 2m 10
v₂ = F / m 5
Let's calculate the kinetic energy of each car
Car 1
K₁ = ½ m v₁²
K₁ = ½ m (F / m 10)²
K₁ = 50 F² / m
Car2
K₂ = ½ 2m v₂²
K₂ = m (F / m 5)²
K₂ = 25 F² / m
In this case we see that the kinetic energy of car 1 is greater than that of car 2
Let's calculate the moment
Car 1
P₁ = m v₁
P₁ = m F / m 10
P₁ = 10 F
Car 2
P₂ = 2m v₂
P₂ = 2m F / m 5
P₂ = 10 F
In this case the moment of the two cars is the same