A set of crash tests consists of running a test car moving at a speed of 11.6 m/s (25.5 m/h) into a solid wall. Strapped securely in an advanced seat belt system, a 61.0 kg (134.2 lbs) dummy is found to move a distance of 0.750 m from the moment the car touches the wall to the time the car is stopped. Calculate the size of the average force which acts on the dummy during that time.

answer for sure =5.472×103 N

part 2: Using the direction of motion as positive direction, calculate the average acceleration of the dummy during that time (in g's) (use 1g=9.8 m/s2).
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To calculate the average force acting on the dummy during the crash test, you can use Newton's second law of motion, which states that force is equal to the mass of an object multiplied by its acceleration:

Force = mass × acceleration

We are given the mass of the dummy, which is 61.0 kg, and the distance it moves, which is 0.750 m. Since the car comes to a complete stop, the final velocity of the dummy is 0 m/s.

To find the acceleration, we can use the kinematic equation:

Final velocity^2 = Initial velocity^2 + 2 × acceleration × distance

Since the initial velocity is 11.6 m/s and the final velocity is 0 m/s, and plugging in the distance as 0.750 m, we can solve for acceleration:

0^2 = 11.6^2 + 2 × acceleration × 0.750
0 = 134.56 + 1.5 × acceleration
1.5 × acceleration = -134.56
acceleration = -134.56 / 1.5
acceleration ≈ -89.7 m/s^2

Since we are interested in the magnitude of acceleration, we can consider it as positive:

acceleration = 89.7 m/s^2

Now let's convert this acceleration to g's using the conversion factor given:

1 g = 9.8 m/s^2

average acceleration in g's = acceleration / (9.8 m/s^2)
average acceleration in g's = 89.7 / 9.8
average acceleration in g's ≈ 9.16 g's

So, the average acceleration of the dummy during that time is approximately 9.16 g's.

To find the average force acting on the dummy during the time of the collision, we can use the equation:

Average force = mass × acceleration

The mass of the dummy is given as 61.0 kg.

To calculate the acceleration, we need to find the change in velocity of the dummy during the collision. Since the car is brought to a stop, the change in velocity is equal to the initial velocity (11.6 m/s) at which the car is moving.

Hence, the average acceleration can be calculated as:

Average acceleration = change in velocity / time

The time is given as the distance moved divided by the initial velocity:

Time = distance / initial velocity

Plugging in the given values:

Time = 0.750 m / 11.6 m/s

Now, we can calculate the average acceleration:

Average acceleration = 11.6 m/s / (0.750 m / 11.6 m/s)

Average acceleration ≈ 11.6 m/s × 15.47 s/m

Average acceleration ≈ 179.3 m/s^2

To convert this to g's, we divide by the acceleration due to gravity:

Average acceleration ≈ 179.3 m/s^2 / 9.8 m/s^2

Average acceleration ≈ 18.3 g's

Therefore, the average acceleration of the dummy during the collision is approximately 18.3 g's.