Acceleration and Free Fall

Acceleration describes a change in velocity. An object accelerates when it speeds up, slows down, or turns, even if its speedometer reading stays the same during the turn.

This lesson supports Chapter 3 of Physics for Beginners. Keep the physical picture in view, write the units, and check the direction of every vector before trusting a calculation.

Acceleration compares two velocities

Average acceleration is \[a=\frac{\Delta v}{\Delta t}=\frac{v_f-v_i}{\Delta t}.\] Its SI unit is meters per second squared. The sign depends on the chosen positive direction. A negative acceleration does not automatically mean an object is slowing down. If velocity and acceleration have opposite signs, speed decreases. If their signs match, speed increases.

Free fall has a nearly constant acceleration

Near Earth’s surface and with air resistance ignored, every freely falling object has the same downward acceleration, \(g\approx9.8\text{ m/s}^2\). Mass does not change this ideal acceleration. A dropped ball begins with zero vertical velocity. A ball thrown upward slows as it rises, reaches zero vertical velocity for an instant, and then speeds up downward.

Separate horizontal and vertical motion

In ideal projectile motion, horizontal velocity stays constant while gravity changes the vertical velocity. Treat the two directions separately, then connect them through the same elapsed time. This keeps signs and components from getting mixed together.

Worked example

A bicycle speeds up from \(4\text{ m/s}\) to \(10\text{ m/s}\) in \(3\text{ s}\). Its average acceleration is \[a=\frac{10-4}{3}=2\text{ m/s}^2.\] The positive result agrees with the bicycle’s increasing velocity in the chosen positive direction.

Watch the idea in action

The Organic Chemistry Tutor gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. Write the formula for average acceleration.
2. What is the SI unit of acceleration?
3. What is \(g\) near Earth’s surface?
4. At the top of an upward toss, what is the ball’s vertical velocity?
5. Does greater mass produce greater ideal free-fall acceleration?
6. When does an object’s speed decrease?

Answers

1. \(a=(v_f-v_i)/\Delta t\).
2. Meters per second squared.
3. About \(9.8\text{ m/s}^2\) downward.
4. Zero for an instant.
5. No.
6. When velocity and acceleration point in opposite directions.

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