1) Impulse: -32,000 kg m/s
The impulse acting on the car is equal to the change in momentum of the car:
[tex]I= \Delta p = m (v-u)[/tex]
where in this problem we have
m = 1000 kg is the mass of the car
v = 0 m/s is the final velocity of the car
u = 32 m/s is the initial velocity of the car
Substituting values into the equation, we find
[tex]I=(1000 kg)(0-32 m/s)=-32,000 kg m/s[/tex]
2) -4751 N
The impulse exerted on the car is also equal to the product between the average force, F, and the duration of the collision, t:
[tex]I=Ft[/tex]
where in this situation we know
[tex]I=-32,000 kg m/s[/tex] is the impulse
t = 7 s is the duration of the collision
Solving the formula for F, we find the average force:
[tex]F=\frac{I}{t}=\frac{-32,000 kg m/s}{7 s}=-4,571 N[/tex]
and the negative sign means that the force is in the opposite direction to the motion of the car.
