A force of -9200 N is used to stop 1500 kg car traveling at 23 m/s. What braking distance is need to bring the car to a halt?
(Braking force) x (distance) = Work done = (Loss of kinetic energy)
Solve for the distance.
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To find the braking distance needed to bring the car to a halt, we can use the following formula:
Braking Force * Braking Distance = (1/2) * Mass * Velocity^2
Given:
Force = -9200 N (negative sign indicates that the force is in the opposite direction of motion)
Mass = 1500 kg
Velocity = 23 m/s
Rearranging the formula, we have:
Braking Distance = [ (1/2) * (Mass * Velocity^2) ] / |Braking Force|
Substituting the given values:
Braking Distance = [ (1/2) * (1500 kg * (23 m/s)^2 ) ] / | -9200 N |
Calculating further,
Braking Distance = [ (1/2) * (1500 * 529) ] / 9200
Braking Distance = (1/2) * 793500 / 9200
Braking Distance = 793500 / 18400
Braking Distance = 43.12 m (rounded to two decimal places)
Therefore, the braking distance needed to bring the car to a halt is approximately 43.12 meters.
To find the braking distance needed to bring the car to a halt, we can use the equations of motion and Newton's second law. Here's how we can solve it step-by-step:
Step 1: Identify the given information:
- Force (F) = -9200 N (negative sign indicates the force is opposite to the direction of motion).
- Mass (m) = 1500 kg.
- Initial velocity (u) = 23 m/s.
- Final velocity (v) = 0 m/s (since we want to bring the car to a halt).
Step 2: Understand the relationship between force, mass, and acceleration:
Newton's second law states that the force applied to an object is equal to the mass of the object multiplied by its acceleration (F = m * a). We can rearrange this equation to solve for acceleration (a) by dividing both sides by the mass: a = F / m.
Step 3: Calculate the acceleration:
Using the equation above, we can find the acceleration: a = -9200 N / 1500 kg.
Step 4: Use the equations of motion to find the braking distance:
The equations of motion involve the initial velocity, final velocity, acceleration, and distance. One of these equations is: v^2 = u^2 + 2ad, where v is final velocity, u is initial velocity, a is acceleration, and d is distance. Rearranging this equation, we get: d = (v^2 - u^2) / (2a). Since v = 0 m/s, we can simplify the equation further to: d = -u^2 / (2a).
Step 5: Calculate the braking distance:
Substituting the values into the equation, we get: d = -(23 m/s)^2 / (2 * a).
Now, we can substitute the acceleration value we calculated in step 3 into the equation to find the braking distance.