Rectilinear Motion

Position, velocity, and acceleration in uniform and uniformly accelerated rectilinear motion.

General idea of the topic

In rectilinear motion the trajectory is a straight line and the position is described with a single coordinate. Depending on whether there is acceleration, two basic models appear: uniform motion, with constant velocity, and uniformly accelerated motion, with constant acceleration.

The topic develops both and applies the second to vertical fall under gravity, where the acceleration is that of gravity, directed downward. The velocity against time graph is a straight line, whose slope is the acceleration and whose area gives the displacement.

What you will truly understand

By the end you will be able to write and use the equations of position and velocity as functions of time, as well as Torricelli's equation, which relates velocity and displacement without involving time, and solve problems of overtaking, braking and vertical throws.

You will also be able to interpret the sign of velocity and acceleration.

Recommended learning route

1. URM: constant velocity, position linear in time and graphs.
2. UARM: constant acceleration, equations and graphs of the three quantities.
3. Vertical motion under gravity: free fall and upward throw with constant gravity, maximum height and flight time.

Physical criterion you must acquire

The essential criterion is to fix the origin and the positive direction before substituting data: the sign of the velocity, the acceleration and gravity follows from that choice. In a vertical throw, the velocity is zero at the highest point but the acceleration is still that of gravity, and the rise time equals the fall time back to the same level.

Connection with real problems

• vehicle braking.
• falling objects.
• elevators and trains.
• races and overtaking.

Final goal of the topic

The final goal is to solve any rectilinear motion problem, choose the equation that contains the known quantities and interpret the result.