Finding Distance Traveled with Given Acceleration and Initial Velocity

In summary, the problem asks for the distance a car travels while stopping, given an acceleration of -4t and an initial velocity of 32m/s. By integrating the acceleration to find velocity and then integrating velocity to find displacement, we can solve for the distance traveled. The choice of coordinate system does not affect the solution.
  • #1
uradnky
30
0

Homework Statement



In coming to a stop the acceleration of a car is given as a= -4t. If it is traveling at 32m/s when the brakes are applied, how far does is travel while stopping?


The Attempt at a Solution



1.) Integrate acceleration to find velocity as a function of time

v= -2t^2 + C1

at t=0 , v = 32m/s

v = -2t^2 + 32


2.) Integrate velocity to find displacement as a funtion of time

s = (2/3)(t^3) + 32t + C2.


This is where I get stuck.

Is it correct to assume that at t=0 , s will be zero and therefore C2 is zero?
 
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  • #2
It's your coordinate system so it's your choice! The problem asks for the distance the car travels- that is the difference between s when the car stops and s when the car is going 32 m/s. Yes you can take "s= 0" to be the point at which the car is going 32 m/s. In fact, if you take s to be any number you like, when you do the subtraction, that number will cancel.
 

What is the purpose of using integrals in scientific applications?

Integrals are used to calculate the total area under a curve, which is useful in many scientific fields such as physics, engineering, economics, and more. They can also be used to find the volume and surface area of three-dimensional objects and to solve various optimization problems.

How are integrals used in physics?

In physics, integrals are used to calculate quantities such as work, energy, and momentum. They are also used to find the center of mass and the moment of inertia of an object. Integrals are essential in solving many equations and problems in classical mechanics, electromagnetism, and other branches of physics.

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Integrals have a wide range of real-life applications, including calculating the area under a population growth curve, finding the average velocity of an object, determining the amount of medication in a patient's bloodstream, and predicting the value of investments using compound interest. They are also used in signal processing, image processing, and data analysis.

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