Graphs 9

The position of a particle moving in a straight line is given by , where is the displacement in metres and is the time in seconds.

Write down the velocity of the particle.

Differentiate with respect to .

A particle moves along a straight line. Its displacement after seconds is given by , where is in metres.

The velocity of a particle is given by , where is in seconds. Find the acceleration of the particle when .

Consider the cubic function . A stationary point occurs when the gradient is zero.

The table below gives the values of y for the curve at different points:

Use the table to estimate the gradient (rate of change) between the points where and . Give your answer in simplest form.

What is the value of the gradient at a stationary point of a curve?

Differentiate with respect to . Give your answer in terms of .

The curve has stationary points.

Find the coordinates of the stationary points and determine whether each is a maximum or a minimum.

A particle moves along a straight line and its displacement from a fixed point at time seconds is given by .

Explain how you would find the velocity and acceleration of the particle at . Write down the values.