Coaching Centre
Chapter 7: Motion and rates Notes
Displacement, velocity and acceleration as derivatives, motion found by integration, interpreting rates of change and concavity in context, total change from a rate, and exponential growth and decay.
Sections
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7A Velocity and acceleration Mastered
Displacement, velocity and acceleration for motion in a straight line, distance versus displacement, average velocity and speed, when a particle is at rest, and when it is speeding up.
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7B Motion and integration Mastered
Finding velocity and displacement by integrating acceleration and velocity, using initial conditions, and motion under gravity.
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7C Rates and differentiation Mastered
Interpreting the first and second derivatives of a quantity over time, describing changes in words such as increasing at a decreasing rate, and the meaning of concavity and points of inflection in a model.
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7D Rates and integration Mastered
Finding a quantity from its rate of change by integration, total change as the area under a rate graph, and rates involving exponential functions such as a flow that dies away.
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7E Exponential growth and decay Mastered
The differential equation dN/dt = kN and its solution N = N0 e^kt, finding the growth constant, solving growth and decay problems, rates of growth, and half-life.