Free Fall, Relative Velocity and Changing Acceleration

Name: Free Fall, Relative Velocity and Changing Acceleration
Author: StemPy Lab

A ball thrown up stops for a moment at the top, and a car seems to stand still when another car goes at the same speed beside it. In this course we study free fall with the acceleration due to gravity, we find the velocity of one body as seen from another, and we meet the first use of calculus in physics, for a body whose acceleration changes with time.

3 lessons, about 1 h 15 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Free fall under gravity
Near the Earth, every falling body, heavy or light, has the same downward acceleration $g = 9.8\ \text{m/s}^2$ if the air can be ignored. Free fall is uniform acceleration, so the equations of motion apply with $a = -g$ (taking up as positive). A ball thrown up has zero velocity at the top but still the acceleration $g$ ; its way up and way down take equal times.
1 simulation2 practice questions1 Python program5 problems1 Python lab1 question set
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Lesson 2about 25 min
Relative velocity in one dimension
The velocity of A as seen from B is $v_{AB} = v_A - v_B$ . Moving the same way, the relative speed is the difference of the speeds; moving towards each other, it is their sum. Questions about overtaking, crossing trains and catching up become simple when you sit on one body and watch the other move at the relative velocity.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Motion with changing acceleration, using calculus
When the acceleration changes, the equations of uniform acceleration fail and calculus takes over. Differentiating the position gives the velocity, $v = dx/dt$ , and differentiating again gives the acceleration, $a = dv/dt$ . Going the other way, integrating the acceleration gives the change in velocity (the area under the acceleration-time graph), and integrating the velocity gives the displacement.
1 simulation2 practice questions1 Python program3 problems1 Python lab1 note
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Free Fall and Relative Motion: Practice Paper

20 questions · 40 min

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← Acceleration and the Equations of Motion Relative Motion →

More onMechanics › Motion in a Straight Line Mechanics › Gravitation Mechanics › Relative Motion

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Free Fall, Relative Velocity and Changing Acceleration

Course outline (3 lessons)

Free fall under gravity

Relative velocity in one dimension

Motion with changing acceleration, using calculus

Test Your Learning

Your teacher

Discussion (0)