Acceleration: how force changes velocity

One cart, one story

We continue the cart story from Motion and Graphs. Now ask not only “how did it move?” but “which objects changed its motion?” Link each new word to a visible scene before using an equation. Numbers on the support map are given teaching values, not a replacement for your own measurements.

A cart begins at rest. A gentle push makes it speed up: in equal time intervals it covers more and more distance. Before using a formula, define “speed up”: velocity changes. Slowing down and turning also change velocity. Our model, however, is limited to a straight track and constant net force.

What the words mean

Acceleration a is change in signed velocity per unit time. The unit m/s² means how many m/s velocity changes each second when acceleration is constant. Newton’s second law for a constant-mass object is FΣ = ma, so a = FΣ/m. Force and acceleration point the same way; velocity need not. Mass is a measure of inertia, not an opposing force.

Check the numbers and limits

Worked model: the cart has mass 0.5 kg and a horizontal net force 2 N right. a = 2 N / 0.5 kg = 4 m/s² right, because 1 N = 1 kg·m/s². Starting at zero velocity with constant acceleration, it has 4 m/s after 1 s and 8 m/s after 2 s. These are not observations of a real school cart: resistance is already included in the net force or ignored.

Try it yourself

Make a table with t = 0, 1, 2 s and v = 0, 4, 8 m/s. Find each change of velocity. If mass becomes 1 kg with the same 2 N, what acceleration follows? Do not put these velocities on the position graph from the previous block: that graph uses different worked data.

A common trap

Do not add 2 N to 0.5 kg: the units differ. Acceleration of 4 m/s² is not a velocity of 4 m/s; it is the rate at which velocity changes.

Support map

Check without hints

Cover the calculation. Name the object receiving forces, their sources, and the chosen positive direction. Rebuild the arithmetic with units. Change one given number and explain which conclusion changes. If you did not run a real trial, write “worked model” in your notebook.

Notebook entry

Write four lines: “What did I see?”, “What was given?”, “What did I calculate?”, and “Which assumptions does this conclusion need?” This separates observation from model and lets you revisit an error later.

Next lesson: Friction and resistance: where did the push go?