A1400 kg car moving at 6.6 m/s is initially traveling north in the positive y direction.
after completing a 90° right-hand turn to the positive x direction in 4.9 s, the inattentive operator drives into a tree, which stops the car in 430 ms.

what is the magnitude of the impulse on the car :

(a) due to the turn and (b) due to the collision?

what is the magnitude of the average force that acts on the car (c) during the turn and (d) during the collision?

(e) what is the angle between the average force in (c) and the positive x direction?

a) J = 13067 kg*m/s

b) J = 9240 kg*m/s

c) F = 2666.73 N

d) F = 21488.37 N

e) 135°

Explanation:

We know that the impulse could be calculated by:

J = ΔP

where ΔP is the change in the linear momentum:

ΔP =

Also:

P = MV

Where M is the mass and V is the velocity.

so:

J=

where is the final velocity and is the inicial velocity

a)The impluse from turn is:

On the turn, and , the magnitude of the impulse on direction x and y are:

So, using pythagoras theorem the magnitude of the impulse is:

J =

J = 13067 kg*m/s

b) The impluse from the collision is:

J = 0 - (1400)(6.6)

J = 9240 kg*m/s

c) Using the next equation:

FΔt = J

where F is the force, Δt is the time and J is the impulse.

Replacing J by the impulse due to the turn, Δt by 4.9s and solving for F we have that:

F = J / Δt

F = 13067 / 4.9 s

F = 2666.73 N

d) At the same way, replacing J by the impulse during the collision, Δt by 0.43s and solving for F we have that:

F = J / Δt

F = 9240 / 0.43

F = 21488.37 N

e) The force have the same direction than the impulse due to the turn, Then, if the impulse have a direction of -45°, the force have -45° or 135°

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.