Question

If the magnitudes of acceleration of each car during the collision averaged 28 m/s², determine the time interval needed to stop.

a) Clearly define the scenario involving the collision and the acceleration of the cars.
b) Instruct the respondent to calculate the time interval needed for each car to come to a stop given an average acceleration of 28 m/s².
c) Encourage a step-by-step explanation or calculation process, demonstrating an understanding of the relationship between acceleration, time, and stopping distance.

Ensure clarity in the question to prompt an accurate calculation and explanation of the time interval needed for the cars to stop during the collision.

Answer 1

To calculate the time required for a car to stop with an average deceleration of 28 m/s², we must know the initial velocity and apply the formula Δt = Δv/a with Δv being the negative of the initial velocity. Without the initial velocity's value, the stopping time can only be expressed as a function of that velocity.

Step-by-step explanation:

We are tasked with determining the time interval required for a car to come to a stop during a collision, given an average acceleration of 28 m/s². The scenario involves a collision where each car has a deceleration with a magnitude of 28 m/s². The relationship used to find the stopping time is the kinematic equation: a = Δv/Δt, where 'a' is acceleration, Δv is the change in velocity, and Δt is the change in time. In this case, the cars go from their initial velocity to a stop (velocity of 0 m/s).

Step-by-Step Calculation Process

1. Identify the initial velocity (v₀) of the cars before the collision. If not given, assume an initial velocity.
2. As the final velocity (v) will be 0 m/s (since the cars come to a stop), calculate the change in velocity (Δv), which is simply the negative of the initial velocity.
3. Use the average acceleration formula: a = Δv/Δt. Rearrange this formula to solve for the time interval (Δt): Δt = Δv/a.
4. Insert the values for Δv (which is -v₀) and 'a' (which is 28 m/s²) into the formula.
5. The result is the time required for the cars to come to a full stop during the collision.

It is crucial to note that the exact value of the initial velocity is essential for an accurate calculation of the stopping time. If it is not provided, one can only calculate the stopping time as a function of the initial velocity.