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To avoid an accident, a driver with a mass of 60 kg applies his brakes and decelerates ; from 30m/s to 1m/s in 2 seconds. How much force was absorbed by his seat belt?

Question

To avoid an accident, a driver with a mass
of 60 kg applies his brakes and
decelerates ; from 30m/s to 1m/s in 2
seconds. How much force was absorbed
by his seat belt?

To avoid an accident, a driver with a mass of 60 kg applies his brakes and decelerates ; from 30m/s to 1m/s in 2 seconds. How much force was absorbed by his seat belt?

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LydiaMaster · Tutor for 5 years

Answer

<p> Using these formulas, the force absorbed by the seatbelt is 870 Newtons.</p>

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<p> This question references Newton's Second Law of motion, which states that the force, F, experienced by a person is equal to the mass, m, times the rate of change of velocity or acceleration, a. That is, \( F = m*a \). The acceleration, a, of an object changing its velocity, v, in a given time, t, is calculates as reduction in speed over time or \( a = \Delta v / t \).<br /><br />The driver's change in velocity (Δv) equals to the initial speed (30 m/s) minus the final speed (1 m/s). So, Δv = 30 m/s - 1 m/s = 29 m/s. <br /><br />The given time interval as 2 seconds.<br /><br />Now we have all the necessary values to calculate acceleration \( a = \Delta v / t = 29 m/s / 2 s = 14.5 m/s.\,\,^2 \).<br /><br />With the driver's mass (60 kg) and the calculated acceleration (a), force (f,) can be calculated using the formula \( F= m * a \).<br /><br />So, inserting the given numbers of \( F = 60 kg * 14.5 m/s\, ^2 \), we can calculate the total force absorbed by the seat belt."."</p>
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