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 50 km/h (31 mph). A new model of mass 1400 kg takes 0.18 s from the time of impact until it is brought to rest. Calculate the average force exerted on the car by the barrier. Calculate the average deceleration of the car.

force*time=changeofmomentum

solve for force.

To calculate the average force exerted on the car by the barrier, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (mΔv) over time (t). Mathematically, it can be expressed as:

F = (m * Δv) / t

Step 1: Calculate the change in velocity (Δv):

Given that the car is brought to rest, the change in velocity (Δv) is equal to the initial velocity (v) of 31 mph (or 13.8 m/s) since the car is moving towards the barrier and is brought to rest.

Δv = 13.8 m/s

Step 2: Plug in the values into the formula and calculate the force:

F = (m * Δv) / t
F = (1400 kg * 13.8 m/s) / 0.18 s
F ≈ 130,666.67 N

The average force exerted on the car by the barrier is approximately 130,666.67 Newtons.

Now, let's calculate the average deceleration of the car. Deceleration (a) can be calculated using the formula:

a = Δv / t

Step 1: Plug in the values into the formula and calculate the deceleration:

a = Δv / t
a = 13.8 m/s / 0.18 s
a = 76.67 m/s^2

The average deceleration of the car is approximately 76.67 m/s^2.