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?

Answer 1

The best estimate of the speed of the particle at time t=20 minutes cannot be determined based on the given information.

Step-by-step explanation:

The best estimate of the speed of the particle at time t=20 minutes can be found by finding the derivative of the position function. Since the position function is given as x(t), the derivative with respect to t will give the speed function v(t). Therefore, we need to find v(t) and evaluate it at t=20 minutes.

First, let's find the velocity function by taking the derivative of x(t):

v(t) = dx/dt

Since the position function is given as a linear function, the velocity function will also be linear. The derivative of a linear function is a constant, which represents the slope of the line. Therefore, the velocity function will be a constant value.

To find the velocity at t=20 minutes, we need to find the slope of the line representing the position function. Since the position function is not given in the question, we do not have enough information to determine the best estimate of the speed at t=20 minutes.