Question

The position of a particle moving to the right on the x-axis is given by x(t), where x(t) is measured in inches and t is measured in minutes for 0≤t≤100. If y=x(t) is a linear function, which of the following would most likely give the best estimate of the speed of the particle, in inches per minute, at time t=20 minutes?

A. x(20)x(20)
B. x(20)20x(20)20
C. x(21)−x(19)x(21)−x(19)

The slope of the graph of y=x(t)

Answer 1

The slope of the graph of y=x(t)

Explanation:

The speed's equation is the derivative of the position.

Position

y = x(t)

Linear function.

So

y = ax(t)

In which a is the slope

The derivative of y is:

y = a

Which is the slope

This means that the speed of the particle is constant.

So the answer is:

The slope of the graph of y=x(t)