Final answer:
The magnitude of impulse during a car crash can be determined by the change in momentum or by multiplying the average force by the time interval over which it acts. By using impulse-momentum theorem, one can solve for the initial speed of the car before impact.
Step-by-step explanation:
The magnitude of the impulse exerted by a car on a wall during a crash can be found using the formula impulse (J) = change in momentum (Δp). This is also equal to the force (F) exerted over the time interval (Δt) the force acts, J = F Δt. To find the initial speed of the car prior to collision, assuming that the car stops (final velocity is zero), we can re-arrange the impulse-momentum theorem to solve for initial velocity (v_i).
As an example, if a car of mass 2500 kg is brought to rest by a wall exerting a force of 740,000 N over 0.22 seconds, the impulse would be:
- Impulse = Force × Time
- Impulse = 740,000 N × 0.22 s = 162,800 kg m/s
Since impulse equals change in momentum (m × Δv), and the final velocity (v_f) is 0 m/s, we set up the equation:
- 162,800 kg m/s = 2500 kg × (v_i - 0 m/s)
- Initial velocity (v_i) = 162,800 kg m/s / 2500 kg
- Initial velocity (v_i) = 65.12 m/s
To convert this to km/h, we multiply by 3.6:
- v_i = 65.12 m/s × 3.6 = 234.43 km/h
Therefore, the initial speed of the car was approximately 234.43 km/h.