You are the design engineer in charge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 56 km/h (35mph ). A new model of mass 1900 kg takes 0.15 s from the time of impact until it is brought to rest.

1. Calculate the average force exerted on the car by the barrier.

2. Calculate the average deceleration of the car.

To calculate the average force exerted on the car by the barrier, you can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). To find the acceleration, you can use the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time.

1. First, convert the speed from km/h to m/s by dividing 56 km/h by 3.6:
56 km/h ÷ 3.6 = 15.6 m/s

2. Next, calculate the change in velocity by subtracting the final velocity (0 m/s) from the initial velocity (15.6 m/s):
Δv = 0 m/s - 15.6 m/s = -15.6 m/s

3. Now, substitute the values into the formula for acceleration:
a = -15.6 m/s ÷ 0.15 s = -104 m/s² (negative because the car is decelerating)

4. Finally, use Newton's second law to calculate the average force exerted on the car:
F = m * a = 1900 kg * -104 m/s² = -197,600 N (negative because the force is in the opposite direction of motion)

Therefore, the average force exerted on the car by the barrier is approximately -197,600 N (or approximately 197.6 kN).

To calculate the average deceleration of the car, you have already found the value in step 3 above: -104 m/s². Therefore, the average deceleration of the car is -104 m/s².

To calculate the average force exerted on the car by the barrier, we can first use the kinematic equation:

\[ v = u + at \]

Where:
- v is the final velocity of the car (0 m/s, as it is brought to rest)
- u is the initial velocity of the car (56 km/h or 15.6 m/s)
- a is the average acceleration of the car
- t is the time taken by the car to come to rest (0.15 s)

Rearranging the equation to solve for acceleration (a):

\[ a = \frac{{v - u}}{t} \]

Substituting the values into the equation:

\[ a = \frac{{0 - 15.6}}{0.15} \]

Simplifying:

\[ a = -104 \, \text{m/s}^2 \]

The negative sign indicates deceleration (decreasing velocity).

1. Now, to calculate the average force exerted on the car by the barrier, we can use Newton's second law of motion:

\[ F = ma \]

Where:
- F is the force exerted on the car (what we want to find)
- m is the mass of the car (1900 kg)
- a is the average deceleration of the car (-104 m/s^2)

Substituting the given values into the equation:

\[ F = 1900 \times -104 \]

Calculating:

\[ F = -197,600 \, \text{N} \]

The negative sign indicates that the force is being exerted in the opposite direction to the car's initial motion (deceleration force).

2. To calculate the average deceleration of the car, we have already determined it to be -104 m/s^2.