To solve this problem, we need to determine whether the car can be brought to rest within the same distance using the same brakes when it is traveling at a speed of 60 km/h.
First, let's convert the speed of the car traveling at 30 km/s to m/s: 30 km/s = 30,000 m/s
We can use the equation of motion to calculate the distance required to bring the car to rest. The equation is:
v² = u² + 2as
Where: v = final velocity (0 m/s, as the car comes to rest) u = initial velocity (30,000 m/s) a = acceleration (unknown) s = distance (8 m)
Rearranging the equation, we have:
a = (v² - u²) / (2s)
Substituting the given values, we find:
a = (0 - (30,000)²) / (2 * 8) a = -30,000,000,000 / 16 a = -1,875,000,000 m/s²
Now, let's determine if the same brakes can bring the car traveling at 60 km/h to rest within 8 meters. First, we need to convert the speed to m/s:
60 km/h = 60,000 m/3,600 s = 16.67 m/s (approximately)
Using the same equation of motion:
a = (v² - u²) / (2s) a = (0 - (16.67)²) / (2 * 8) a = -277.89 m/s² (approximately)
Comparing the accelerations, we see that the acceleration required to stop the car traveling at 60 km/h within 8 meters (-277.89 m/s²) is significantly lower than the acceleration required to stop the car traveling at 30 km/s within the same distance (-1,875,000,000 m/s²).
Therefore, it is not possible to bring the car to rest within 8 meters using the same brakes when it is traveling at a speed of 60 km/h. The car would require a longer stopping distance or stronger brakes to achieve that.