A car moving at 50 km/h goes 15 m before coming to a complete stop after braking. How far will the car go after braking if it is moving at 150 km/h? Assume the same braking force a... A car moving at 50 km/h goes 15 m before coming to a complete stop after braking. How far will the car go after braking if it is moving at 150 km/h? Assume the same braking force as before.
Understand the Problem
The question is asking for the distance a car will travel after braking when moving at a higher speed, given that it travels 15 m at a lower speed under the same braking conditions. It involves understanding the relationship between speed, braking distance, and kinetic energy.
Answer
The car will travel \( 135 \) m after braking at \( 150 \) km/h.
Answer for screen readers
The distance the car will travel after braking at 150 km/h is ( 135 ) m.
Steps to Solve
- Understanding the Relationship Between Speed and Braking Distance
The braking distance of a car is related to the square of its speed. The relationship can be defined as follows:
$$ d \propto v^2 $$
where ( d ) is the braking distance and ( v ) is the speed of the car.
- Calculating the Factor of Increase in Speed
We know the initial speed ( v_1 = 50 ) km/h, and the new speed ( v_2 = 150 ) km/h. First, we will find the ratio of the speeds:
$$ \text{Ratio} = \frac{v_2}{v_1} = \frac{150}{50} = 3 $$
- Finding the Braking Distance at the New Speed
Since the braking distance changes with the square of the speed, we can find the new distance ( d_2 ):
$$ d_2 = d_1 \times \left(\frac{v_2}{v_1}\right)^2 $$
We know ( d_1 = 15 ) m, giving us:
$$ d_2 = 15 \times (3)^2 = 15 \times 9 = 135 \text{ m} $$
The distance the car will travel after braking at 150 km/h is ( 135 ) m.
More Information
When a car's speed increases, the distance it needs to stop grows significantly due to the kinetic energy being proportional to the square of the speed. This means that if you triple the speed, the stopping distance increases by a factor of nine.
Tips
- Neglecting the square relationship: Some may incorrectly assume that braking distance changes linearly with speed rather than quadratically. Remember that distance is proportional to the square of the speed.
- Confusing units: Make sure to keep speeds in the same unit if comparing or converting. Here we kept it in km/h.
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