Distance Formula: Calculate w/ Acceleration & Time

  • Thread starter Thread starter spencerda
  • Start date Start date
  • Tags Tags
    Formula
Click For Summary
SUMMARY

The distance formula for calculating distance under constant acceleration is expressed as d = (1/2)at² + v₀t, where d represents the total distance, a is the acceleration, and v₀ is the initial velocity, which is zero in this case. This formula is derived from calculus by integrating acceleration to obtain velocity and then integrating velocity to obtain position. For non-constant acceleration scenarios, the discussion indicates a need for further exploration of alternative formulas.

PREREQUISITES
  • Understanding of basic physics concepts, specifically kinematics.
  • Familiarity with calculus, particularly integration techniques.
  • Knowledge of the relationship between acceleration, velocity, and distance.
  • Ability to apply mathematical formulas in practical scenarios.
NEXT STEPS
  • Research the equations of motion for non-constant acceleration.
  • Learn about numerical methods for integrating acceleration functions.
  • Explore the concept of instantaneous acceleration and its applications.
  • Study real-world examples of motion under varying acceleration conditions.
USEFUL FOR

Students in physics or engineering, educators teaching kinematics, and anyone interested in understanding motion dynamics under varying conditions.

spencerda
Messages
1
Reaction score
0
I'm doing a project for a science class and need to know how you calculate distance when given acceleration and time (with no beginning velocity).
 
Physics news on Phys.org
Assuming you are talking about a constant acceleration, what you are looking for is

<br /> d=\frac{1}{2}at^2+v_0 t<br />

where d is the total distance traveled, a is the acceleration, v_0 is the initial velocity but you said you will be taking that as zero. If you know calculus, the way you arrive at this formula comes simply from integrating the constant acceleration twice; in other words, with calculus you can say that the integral of acceleration (where the integration variable is time) is velocity, and the integral of velocity (integration variable also time) is position.
 
16180339887 said:
Assuming you are talking about a constant acceleration, .

just wondering what's the formulae if its not constant
 

Similar threads

Relating acceleration to distance and time
  • · Replies 5 ·
Replies
5
Views
3K
Solving Distance Traveled Using Formulas vs. Graphs
  • · Replies 6 ·
Replies
6
Views
2K
Solving for Work Done When Accelerating a Mass
  • · Replies 3 ·
Replies
3
Views
925
(Magnetism) Magnetic pull force on a steel ball
  • · Replies 4 ·
Replies
4
Views
3K
Calculate the Acceleration of this Car
  • · Replies 7 ·
Replies
7
Views
1K
Having a hard time learning Newton's 2nd law
  • · Replies 5 ·
Replies
5
Views
2K
Irodov 1.23 confusion: Calculate distance traveled and time elapsed for this decelerating particle
  • · Replies 2 ·
Replies
2
Views
1K
Velocity Formulas for Projectile Motion
  • · Replies 10 ·
Replies
10
Views
3K
How to calculate freezing time for a moist food by-product (75% water)
  • · Replies 6 ·
Replies
6
Views
924
Minimal rotational kinetic energy for a gyroscope to precess
  • · Replies 33 ·
2
Replies
33
Views
3K