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Answer :
Final answer:
To slow down the car, a force of approximately -8562.5 N is required.
The car travels approximately 29.60 m during its deceleration.
Explanation:
To find the force required to slow down a car, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = m * a). Here, the mass of the car is 1250 kg. To find the acceleration, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken. Rearranging the equation, we have a = (v - u) / t.
Using the given values, the initial velocity (u) is 115 km/h, the final velocity (v) is 30 km/h, and the time (t) is 3.50 s. Converting the velocities to m/s, we have u = 115 km/h * (1000 m/1 km) * (1 h/3600 s) = 31.94 m/s and v = 30 km/h * (1000 m/1 km) * (1 h/3600 s) = 8.33 m/s.
Substituting the values into the equation, a = (8.33 m/s - 31.94 m/s) / 3.50 s ≈ -6.85 m/s^2. The negative sign indicates deceleration. Therefore, the force required to slow down the car can be calculated using F = m * a = 1250 kg * -6.85 m/s^2 ≈ -8562.5 N. The car travels a certain distance during its deceleration, which can be found using the equation d = ut + (1/2) * a * t^2. Substituting the values, d = 31.94 m/s * 3.50 s + (1/2) * -6.85 m/s^2 * (3.50 s)^2 ≈ 29.60 m.
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