Motion in a Plane: Velocity, Acceleration and Relative Motion

Name: Motion in a Plane: Velocity, Acceleration and Relative Motion
Author: StemPy Lab

A boat that points straight across a river does not land straight across. In this course we describe the position, velocity and acceleration of a body that moves in a plane, we find that the two directions of motion do not disturb each other, and we use the relative velocity to solve problems about boats in rivers, rain and an umbrella, and aeroplanes in the wind.

3 lessons, about 1 h 20 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Position, displacement, velocity and acceleration in a plane
The position of a body in a plane is $\vec{r} = x\hat{i} + y\hat{j}$ , and its displacement is the change $\Delta\vec{r}$ . Average velocity is $\Delta\vec{r}/\Delta t$ . As $\Delta t$ shrinks, it becomes the velocity $\vec{v} = d\vec{r}/dt$ , which always points along the tangent to the path. Acceleration is the rate of change of velocity, so a turn at a steady speed is an acceleration too.
1 simulation2 practice questions1 Python program4 problems1 question set
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Lesson 2about 25 min
Motion in a plane with constant acceleration
With a steady acceleration, $\vec{v} = \vec{u} + \vec{a}t$ and $\vec{r} = \vec{u}t + \frac{1}{2}\vec{a}t^2$ . Each equation splits into an $x$ equation and a $y$ equation, which run side by side with the same time. The path is a straight line or a parabola.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 30 min
Relative velocity in two dimensions
The velocity of A relative to B is $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$ . A boat's velocity over the ground is its velocity in the water plus the river's velocity. It crosses fastest when it points straight across, and lands straight opposite only by pointing upstream. Rain seems to slant towards you when you walk, so you tilt your umbrella forward.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Relative Velocity and Plane Motion: Practice Paper

20 questions · 50 min

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Motion in a Plane: Velocity, Acceleration and Relative Motion

Course outline (3 lessons)

Position, displacement, velocity and acceleration in a plane

Motion in a plane with constant acceleration

Relative velocity in two dimensions

Test Your Learning

Your teacher

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