Final answer:
To calculate the deceleration of a passenger compartment that comes to rest in a crash test within 0.20 s, one must subtract the final velocity (which is 0 m/s) from the initial velocity and then divide by the time interval. Without the initial velocity given, the calculation can't be completed, but the formula is deceleration = - Δv / t.
Step-by-step explanation:
To calculate the deceleration of the passenger compartment coming to rest during a crash test, we can use the formula for acceleration (a), which is defined as the change in velocity (Δv) divided by the time (t) it takes for that change to occur. Therefore, deceleration is just negative acceleration.
Since the passenger compartment comes to rest, its final velocity (vf) is 0 m/s. Assuming it was moving initially, we need the initial velocity (vi) to calculate the change in velocity. However, since the initial velocity is not provided in this question, we'll proceed with a general explanation. The change in velocity (Δv) is then vf - vi and the formula for deceleration is:
deceleration = - Δv / t
For any given initial velocity, you would plug that value in as vi and the stopping time provided, 0.20 s, in the formula to find the deceleration.
For example, if a car was moving at 10 m/s before coming to rest in 0.20 s, the deceleration would be:
deceleration = - (0 m/s - 10 m/s) / 0.20 s
deceleration = -10 m/s / 0.20 s = -50 m/s²
This means the passenger compartment would decelerate at a rate of 50 meters per second squared in the negative direction, indicating a slowing down.