Newtonian mechanics

Position, velocity, acceleration

Observe the position, velocity, and acceleration vectors of a moving point, then check the graph against the definitions $v = \Delta x/\Delta t$ and $a = \Delta v/\Delta t$ . Read the numbers at each instant to verify how the three quantities relate.

Middle school

Equipment

Rotatable 3D scene canvas showing the point with velocity (blue) and acceleration (teal) vectors
“Time” slider (in s) and “Parameter” slider (in m/s²)
“Pause”/“Resume” button and the x, v, a readout
Time-evolution plot canvas in section 2

Procedure

Track the point and velocity vector
Drag the section-1 canvas to rotate the view. The orange dot is the object; the blue arrow is the velocity $\vec{v}$ tangent to the path, and the teal arrow is the acceleration $\vec{a}$ . Move the “Time” slider and watch the direction and length of both vectors change with position.
Read values at one instant
Press “Pause” to hold the frame, or drag “Time” to a chosen value. Record the triple from the readout: position x, velocity v, acceleration a at the same instant t. Repeat at two nearby instants and compute $v \approx \Delta x/\Delta t$ to compare with the v reading.
Change the parameter and read the plot
Increase the “Parameter” slider (in m/s²) and look at section 2: the curve changes slope and the blue marker travels along it. The slope of a position–time curve gives velocity; on the velocity graph, the slope of the v–t line gives acceleration $a = \Delta v/\Delta t$ . Check the caption readout under the plot.
Predict and verify
Pick an instant and predict the signs of v and a before looking at the vectors: is the object moving in the positive or negative direction, speeding up or slowing down? Then read the vectors and numbers to check. Remember that acceleration opposite to velocity just means slowing down.

Simulation

Experiment history

Galileo Galilei was the first to measure motion quantitatively: early in the seventeenth century he rolled balls down inclined planes and timed them with a water clock, finding that the distance fallen is proportional to the square of time and that speed grows uniformly. Published in Discorsi e dimostrazioni matematiche (1638), the result founded the concept of constant acceleration. Isaac Newton placed this kinematics in a general framework in the Principia (1687): position, velocity, and acceleration became quantities related by time derivatives,

v = dx/dt

and

a = dv/dt

, using the calculus Newton and Leibniz had developed independently. Mechanical motion was thereby reduced to knowing initial position and velocity plus acceleration as a function of time.

Related physicists

Galileo Galilei Isaac Newton

Equipment

Procedure

Simulation

Experiment history

Related physicists

Related library topics