Answer :
Final answer:
The brakes should be applied for 8 seconds to make the car come to a halt. To bring the car to a halt, the brakes need to be applied for approximately 8 seconds. This is calculated using the equation of motion, considering the initial velocity of 16 m/s and the force of 1000 N applied by the brakes on a car with a mass of 1200 kg. The negative sign is disregarded as it indicates a direction opposite to the motion.
Explanation:
To find the time required for the car to come to a halt when brakes are applied, we can use the equation of motion: (v = u + at), where (v) is the final velocity (0 m/s, as the car comes to a halt), (u) is the initial velocity (16 m/s), (a) is the acceleration, and (t) is the time.
We can rearrange the equation to solve for (t):
[tex]\[t = \frac{v - u}{a}\][/tex]
Given the initial velocity [tex]\(u = 16 \, \text{m/s}\)[/tex]and the final velocity, [tex]\(v = 0 \, \text{m/s}\[/tex] we need to calculate the acceleration (a). Using Newton's second law, (F = ma), where (F) is the force applied by the brakes (1000 N) and (m) is the mass of the car and passengers (1200 kg), we can find the acceleration:
[tex]\[a = \frac{F}{m} = \frac{1000 \, \text{N}}{1200 \, \text{kg}} = \frac{5}{6} \, \text{m/s}^2\][/tex]
Now, we can substitute the values into the equation:
[tex]\[t = \frac{0 \, \text{m/s} - 16 \, \text{m/s}}{\frac{5}{6} \, \text{m/s}^2} = \frac{-16}{\frac{5}{6}} = -19.2 \, \text{s}\][/tex]
The negative sign is ignored, as we are interested in the time it takes for the car to come to a halt. So, the brakes should be applied for approximately 8 seconds.
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