Answer :
Final answer:
The car's acceleration while braking was -2.74 m/s2.
Explanation:
The car's initial speed is given as 50.0 km/h, and it comes to a stop over a distance of 35.0 m. We can find the car's acceleration by using the equation:
Final velocity2 = Initial velocity2 + 2 * acceleration * distance
Plugging in the given values, we have:
02 = (50.0 km/h)2 + 2 * acceleration * 35.0 m
Simplifying this equation, we can convert the initial velocity from km/h to m/s by dividing by 3.6. Then, we can solve for the acceleration:
0 = (50.0 km/h / 3.6 m/s)2 + 2 * acceleration * 35.0 m
0 = (13.9 m/s)2 + 70.0 m * acceleration
Solving for acceleration, we get:
acceleration = - (13.9 m/s)2 / (70.0 m) = -2.74 m/s2
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The car's acceleration in m/s² while it was braking is -2.757 m/s².
The initial velocity (u) of the car = 50 km/h
The distance (s) covered by the car before coming to rest = 35 m
Now, we need to calculate the acceleration of the car while it was braking.
First, we convert the initial velocity of the car from km/h to m/s.
1 km/h = 0.27777777777778 m/s
Therefore, the initial velocity of the car in m/s = 50 × 0.27777777777778 = 13.8889 m/s (approx)
We can use the equation of motion which relates the final velocity (v), initial velocity (u), acceleration (a) and distance (s).
v² = u² + 2as
Here, final velocity (v) = 0 (since the car comes to rest), initial velocity (u) = 13.8889 m/s, distance (s) = 35 m.
Substituting these values in the above equation, we obtain:
0² = (13.8889)² + 2a(35)
0 = 193.0558 + 70a
70a = -193.0558
a = -2.757 m/s² (approx)
Therefore, the acceleration of the car while it was braking was -2.757 m/s². (Note that the negative sign indicates that the car was decelerating or slowing down).
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