How Far Does a Car Travel to Reach 4.61 m/s with Non-Constant Acceleration?

In summary, the conversation discusses solving a differential equation to find the distance traveled by a car that starts with an acceleration of a(s)=k*s^n m/s^2. The values for k, n, and starting speed are given, and the chain rule is used to set up the equation for v(s). It is then suggested to plug in the values and solve for s, but the person is unsure if they should antiderivate first.
  • #1
albert12345
27
0

Homework Statement


A car accelerates with the acceleration a(s)=k*s^n m/s^2
s= distance in m
k = 5,8
n=0,7351
The car starts the acceleration from 0 m/s

How far has the car traveled when it reaches the speed 4,61m/s?

The Attempt at a Solution


When i anti derivate one time i will get dv/dt. Do i put in the distance after that?
 
Physics news on Phys.org
  • #2
adx = adv

Where x is the distance "s"
so I get this:

(1/2)*(x^2) = v2^2 - V1^2

Where v2 is the final speed and v1 is the starting speed=0..

Am i right or wrong?
 
  • #3
Albert12345 said:

The Attempt at a Solution


When i anti derivate one time i will get dv/dt. Do i put in the distance after that?

What do you mean? dv/dt =a, the acceleration.

You have a differential equation dv(s(t))/dt=k*s^n. Write up the left-hand side with applying the chain rule:

dv/dt=dv/ds ds/dt. ds/dt=v, so v dv/ds =ks^n. This is a differential equation for v(s), easy to solve.ehild
 
  • #4
So I just plug in my values here, or do i have to antiderivate first?

v dv/ds =ks^n
 
  • #5
So I just plug in my values here and solve for s, or do i have to antiderivate first?

v dv/ds =ks^n
 
  • #6
How do you want to solve for s? Show your attempt.

ehild
 

FAQ: How Far Does a Car Travel to Reach 4.61 m/s with Non-Constant Acceleration?

What is non constant acceleration?

Non constant acceleration, also known as variable acceleration, refers to a situation where an object's velocity changes at an uneven rate over time. This means that the object's acceleration is not constant, and can either increase or decrease over time.

How is non constant acceleration different from constant acceleration?

The main difference between non constant acceleration and constant acceleration is that in the latter case, the object's velocity changes at a constant rate over time. This means that the object's acceleration remains the same throughout its motion.

What causes non constant acceleration?

Non constant acceleration can be caused by various factors, including changes in the forces acting on an object, changes in the object's mass, or changes in the direction of the object's motion. In general, any change in the object's velocity can result in non constant acceleration.

How can non constant acceleration be calculated?

To calculate non constant acceleration, you can use the equation a = (vf - vi) / t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval. However, this equation only applies if the acceleration is constant, so if the acceleration is non constant, you will need to use more complex equations or graphical methods.

What are some examples of non constant acceleration?

Some examples of non constant acceleration include a car accelerating from a stop, a ball rolling down a hill, or a rocket taking off into space. In all of these cases, the acceleration changes over time due to changes in the forces acting on the objects.

Back
Top