A 1,200 kg car is traveling at 10 m/s. What is the minimum distance at which an automatic braking system needs to activate to avoid hitting a stationary object? (Note: The braking system can decelerate the car at 2 m/s2.)A.2.5 mB.5.0 mC.25 mD.50 mSubmit
Question
A 1,200 kg car is traveling at 10 m/s. What is the minimum distance at which an automatic braking system needs to activate to avoid hitting a stationary object? (Note: The braking system can decelerate the car at 2 m/s2.)A.2.5 mB.5.0 mC.25 mD.50 mSubmit
Solution
To solve this problem, we need to use the formula for stopping distance under constant acceleration (deceleration in this case), which is:
d = (v² - u²) / 2a
where:
- v is the final velocity (0 m/s in this case, because the car comes to a stop),
- u is the initial velocity (10 m/s),
- a is the acceleration (negative in this case because it's deceleration, so -2 m/s²), and
- d is the distance we want to find.
Substituting the given values into the formula, we get:
d = (0 - (10)²) / 2*(-2) = 50 m
So, the minimum distance at which the automatic braking system needs to activate to avoid hitting a stationary object is 50 meters. Therefore, the correct answer is D.50 m.
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