Non-Constant Acceleration Problem

In summary, the Tesla car can travel a distance of 833.3 meters over 10 seconds of constant acceleration.
  • #1
Jewelz
8
0

Homework Statement


A new Tesla is designed that can perform a non-constant acceleration for 10 seconds of motion. The magnitude of the acceleration is given as a(t) = 1 m/s4t2

Starting from rest, how far does the car travel over this 10 second interval?

Homework Equations


This is what is making the question difficult for me. I am unsure what equations to use with a non-constant acceleration.

The Attempt at a Solution


I tried solving it manipulating the constant velocity and acceleration equations, but everything I have tried has been wrong. Even if someone could point me in the right directions equations wise, I'm sure that would help me a lot.

Thanks
 
Physics news on Phys.org
  • #2
Hi, you can find the velocity function respect to ##t## that is ##v(t)=\int_{0}^{t} a(s)ds## and after the space ##x(t)=\int_{0}^{t}v(s)ds##, put ##t=10 s## in ##x(t)## ...
Ssnow
 
  • #3
Jewelz said:

Homework Statement


A new Tesla is designed that can perform a non-constant acceleration for 10 seconds of motion. The magnitude of the acceleration is given as a(t) = 1 m/s4t2

Starting from rest, how far does the car travel over this 10 second interval?

Homework Equations


This is what is making the question difficult for me. I am unsure what equations to use with a non-constant acceleration.

The Attempt at a Solution


I tried solving it manipulating the constant velocity and acceleration equations, but everything I have tried has been wrong. Even if someone could point me in the right directions equations wise, I'm sure that would help me a lot.

Thanks

Your input is hard to read; I assume you mean ##a = k t^2,## where ##k = 1 m/s^4.##

Anyway, you get velocity ##v## by integrating ##a## with respect to ##t##, and then you get position by integrating ##v##. No amount of manipulation of the constant-acceleration formulas can do what you need.
 
Last edited:
  • #4
Ray Vickson said:
Your input is hard to read; I assume you mean ##a = k t^2,## where ##k = 1 m/s^4.##

Anyway, you get velocity ##v## by integrating ##a## with respect to ##t##, and then you get position by integrating ##v##. No amount of manipulation of the constant-acceleration formulas can do what you need.
Your assumption is correct.

After integrating the acceleration function with respect to time, with the bounds of the integral from ##0## to ##t##, I obtained the function ##t^3/3## for the velocity. Integrating that, from 0 to t for the integral, I got ##t^4/12##, and plugging in ##t## (10 seconds), I obtained a final answer of 833.3m traveled.

Does this all sound correct?
 
  • #5
Jewelz said:
Your assumption is correct.

After integrating the acceleration function with respect to time, with the bounds of the integral from ##0## to ##t##, I obtained the function ##t^3/3## for the velocity. Integrating that, from 0 to t for the integral, I got ##t^4/12##, and plugging in ##t## (10 seconds), I obtained a final answer of 833.3m traveled.

Does this all sound correct?

It does.
 
  • #6
Jewelz said:
Your assumption is correct.

After integrating the acceleration function with respect to time, with the bounds of the integral from ##0## to ##t##, I obtained the function ##t^3/3## for the velocity. Integrating that, from 0 to t for the integral, I got ##t^4/12##, and plugging in ##t## (10 seconds), I obtained a final answer of 833.3m traveled.

Does this all sound correct?
Yes, perfect.
 

1. What is non-constant acceleration?

Non-constant acceleration is when an object's velocity changes at a non-uniform rate. This means that the object is accelerating or decelerating at different rates throughout its motion.

2. How is non-constant acceleration different from constant acceleration?

Constant acceleration is when an object's velocity changes at a constant rate. This means that the object is accelerating or decelerating at the same rate throughout its motion. Non-constant acceleration, on the other hand, has varying rates of acceleration or deceleration.

3. What causes non-constant acceleration?

Non-constant acceleration can be caused by various factors such as changes in the applied force, changes in mass, or changes in the direction of motion. For example, a car accelerating and decelerating while driving on a curved road experiences non-constant acceleration due to changes in direction.

4. How is non-constant acceleration calculated?

Non-constant acceleration can be calculated using the formula: acceleration = change in velocity / change in time. However, since the rate of acceleration is not constant, this calculation must be done for small intervals of time and then averaged to get an approximate value.

5. What are some real-life examples of non-constant acceleration?

Some common examples of non-constant acceleration in everyday life include driving in a car, riding a rollercoaster, and throwing a ball. In all of these scenarios, the object experiences changes in velocity at varying rates, resulting in non-constant acceleration.

Similar threads

  • Introductory Physics Homework Help
2
Replies
55
Views
511
  • Introductory Physics Homework Help
Replies
11
Views
885
  • Introductory Physics Homework Help
Replies
5
Views
784
  • Introductory Physics Homework Help
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
14K
  • Introductory Physics Homework Help
3
Replies
98
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
20
Views
2K
Back
Top