High School

The brakes of a car are applied, causing it to slow down at a rate of 11 ft/s². The car stops at a distance of 300 ft. Determine how fast the car was traveling immediately before the brakes were applied.

The speed of the car immediately before the brakes were applied was _____ ft/s.

Answer :

The car was traveling at an initial speed of approximately 81.25 ft/s before the brakes were applied, calculated using the kinematic equation for motion with deceleration and distance covered.

Determining Initial Speed Before Braking

  • To find the initial speed of the car before the brakes were applied, we'll use one of the kinematic equations of motion. The equation to use is:

v² = u² + 2as

  • Where:
  1. v is the final velocity (0 ft/s, since the car stops).
  2. u is the initial velocity (what we're trying to find).
  3. a is the acceleration (-11 ft/s², because the car is decelerating).
  4. s is the distance (300 ft).
  5. Rearranging the equation to solve for u:

0 = u² + 2(-11)(300)

0 = u² - 6600

  • Therefore:

u² = 6600

  • Taking the square root of both sides:

u = √6600 ≈ 81.25 ft/s

So, the initial speed of the car immediately before the brakes were applied was 81.25 ft/s.

The speed of the car immediately before the brakes were applied was 81.24 ft/s.

The given data is given below:

Initial speed = ?

Final speed = 0

Acceleration = -11ft/s²

Time = ?

Distance = 300ft

Using the equation of motion, we have:

final velocity² = initial velocity² + 2 × acceleration × distance

Putting the given values in this formula, we get:

0² = v₀² + 2 × (-11ft/s²) × 300ftv₀²

= 6,600ft²/s²v₀

= √6,600ft²/s²v₀

= 81.24ft/s

Therefore, the speed of the car immediately before the brakes were applied was 81.24 ft/s.

When a car's brakes are applied, it begins to slow down. As a result, it is required to find the initial speed of the car. This issue can be solved using an equation of motion.

Initial velocity, final velocity, acceleration, distance, and time are all variables in the equation of motion. We have the final speed, acceleration, and distance in this problem, and we must determine the initial speed.

We'll substitute the given values into the formula and solve for initial velocity. We can write the equation of motion as follows:

final velocity² = initial velocity² + 2 × acceleration × distance

To calculate the initial velocity of the car, we'll use this formula. We can plug in the final speed as 0, since the car came to a complete stop, and we know that the acceleration was 11ft/s² in the opposite direction of the car's motion because the brakes were applied, and the distance was 300 ft. We obtain the value of initial velocity from this formula.

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