Numerical Question A Car Is Traveling At 18m/s She Sees A Red Light Ahead Her Car Is Capable Of Decelerating At A Rate Of 3.65m/s Square If She Applies Brakes When She Is Only 20.0m From The Intersection When She Sees The Light Will She Be Able To Stop

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Introduction

In this article, we will explore a numerical problem involving a car traveling at a certain speed and decelerating at a specific rate. We will use the concept of kinematics to determine whether the car can stop in time when the driver applies the brakes.

Problem Statement

A car is traveling at a speed of 18 m/s when the driver sees a red light ahead. The car is capable of decelerating at a rate of 3.65 m/s^2. If the driver applies the brakes when the car is only 20.0 m from the intersection, will the car be able to stop in time?

Kinematics Equations

To solve this problem, we will use the kinematics equations, which describe the motion of an object under the influence of a constant acceleration. The equations are:

  • v = u + at
  • s = ut + (1/2)at^2
  • v^2 = u^2 + 2as

where:

  • v is the final velocity
  • u is the initial velocity
  • a is the acceleration
  • t is the time
  • s is the displacement

Solution

We are given the following values:

  • u = 18 m/s (initial velocity)
  • a = -3.65 m/s^2 (deceleration rate)
  • s = 20.0 m (displacement from the intersection)

We need to find the time t it takes for the car to stop. We can use the equation v^2 = u^2 + 2as to solve for t.

v^2 = u^2 + 2as

Substituting the given values, we get:

v^2 = (18 m/s)^2 + 2(-3.65 m/s^2)(20.0 m)

v^2 = 324 + (-146) = 178 m2/s2

Now, we need to find the final velocity v when the car stops. We can set v = 0 m/s, since the car comes to a stop.

0^2 = 178 m2/s2

This equation is not true, which means that the car will not be able to stop in time.

Discussion

In this problem, we used the kinematics equations to determine whether the car can stop in time. We found that the car will not be able to stop in time, since the equation 0^2 = 178 m2/s2 is not true.

This problem illustrates the importance of considering the kinematics of a situation when making decisions. In this case, the driver should have applied the brakes earlier to avoid a collision.

Conclusion

In conclusion, we used the kinematics equations to solve a numerical problem involving a car traveling at a certain speed and decelerating at a specific rate. We found that the car will not be able to stop in time, which highlights the importance of considering the kinematics of a situation when making decisions.

References

  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics (10th ed.). John Wiley & Sons.
  • Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers (10th ed.). Cengage Learning.

Additional Resources

  • Khan Academy: Kinematics
  • MIT OpenCourseWare: Physics I
  • Physics Classroom: Kinematics