Question

A particle is moving along the x-axis, and theposition of the particle at time t is given byx(t), whose graph is shown above. Which ofthe following is the best estimate for the speedof the particle at time t=6?

Answer 1

At t = 6, the speed is 5/4

Which is the speed at t = 6?

Time t is meaured in the horizontal axis, so first we need to look at that axis.

We want to find the speed at t = 6, we can see that in that value the position changes linearly, so we only need to find the slope of that line.

Two points on that graph are (0, 10) and (8, 20), then the speed of the particle is:

(20 - 10)/(8- 0) = 5/4

The correct option is the last one.

Answer 2

We are given the graph of a particle moving along the x-axis.

The position of the particle is on the y-axis and the time is on the x-axis.

We are asked to find the best estimate for the speed of the particle at time t = 6?

The speed of the particle is given by

`s=(x)/(t)`

Where x is the distance and t is the time.

From the graph, at t = 6, the distance is approximately x = 20

`s=(20)/(6)=(10)/(3)`

Therefore, the best estimate for the speed of the particle is 10/3