Displacement as a function of velocity, acceleration and time.

Displacement
Choose a Calculation
v0 = 
a = 
t = 
Units:
Answer:
x = 
v0 = 
a = 
t = 

Equation for this Calculation:

x = v0t + ½at2

Where:
x = displacement
v0 = initial velocity
a = acceleration
t = time

 

The displacement calculator finds the displacement (distance traveled) by an object using its initial velocity, acceleration, and time traveled. The equation used is x = v0t + ½at2; it is manipulated below to show how to solve for each individual variable.

Formula for displacement as a function of velocity, acceleration and time.

  • x = v0t + ½at2
    • x = displacement
    • v0 = initial velocity
    • a = acceleration
    • t = time

Displacement calculations used in calculator:

Solving for the different variables we can use the following formulas:

  • Given v0, t and a calculate x
    Given initial velocity, time and acceleration calculate the displacement.
    • x = v0t + ½at2
  • Given x, t and a calculate v0
    Given displacement, time and acceleration calculate the final velocity.
    • v0 = x/t - ½at
  • Given a, v0 and x calculate t
    Given acceleration, initial velocity and displacement calculate the time.
    • ½at2 + v0t - x = 0
  • Given x, t and v0 calculate a
    Given displacement, time and initial velocity calculate the acceleration.
    • a = 2x/t2 - 2v0/t

Displacement Problem 1: A car traveling at 25 m/s begins accelerating at 3 m/s2 for 4 seconds. How far does the car travel in the 4 seconds?

The three variables needed for distance are given as Vo (25 m/s), A(3 m/s2), and T(4 sec).

x = v0t + ½at2. X=25 (m/s)*4 (sec) + ½*3 (m/s2)*(4 (sec))2= 124 meters

Displacement Problem 2: It takes a plane, with an initial speed of 20 m/s, 8 seconds to reach the end of the runway. If the plane accelerates at 10 m/s2, how long is the runway?

x = v0t + ½at2. X= 20 (m/s)*8(sec)+ ½*10(m/s2) *(8(sec))2 = 600 meters

 

Cite this content, page or calculator as:

Furey, Edward "Displacement as a function of Velocity, Acceleration and Time" From http://www.CalculatorSoup.com - Online Calculator Resource.