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 centimeters and t is measured in seconds for 0≤t≤50. 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 centimeters per second, at time t = 10 seconds?

a. The slope of the line through (0, x(0)) and (10, x(10)).
b. The slope of the line through (0, x(0)) and (50, x(50)).
c. The slope of the line through (10, x(10)) and (20, x(20)).
d. The slope of the line through (20, x(20)) and (30, x(30)).

Answer 1

The best estimate of the speed of the particle at time t = 10 seconds can be found by calculating the slope of the line through two points on the position graph.

Step-by-step explanation:

The best estimate of the speed of the particle at time t = 10 seconds can be found by calculating the slope of the line through two points on the position graph. The correct option would be (c), which involves finding the slope of the line through (10, x(10)) and (20, x(20)).

To calculate the slope, we use the formula: slope = (change in y) / (change in x). In this case, the change in x is 20 - 10 = 10 seconds, and the change in y is x(20) - x(10) centimeters. We can substitute the values into the formula to find the slope.

Once we have the slope, we can interpret it as the average velocity of the particle between t = 10 seconds and t = 20 seconds. Since velocity is a vector quantity that includes direction, the slope itself does not give us the exact direction, but it tells us whether the particle is moving faster or slower.