Question

The displacement (in feet) of a particle moving in a straight line is given by

s= 1/2t²−6t+23, where t is measured in seconds. Find the average velocity over each time interval:
a) Differentiated function
b) Indefinite integral
c) Area under the curve
d) Slope of the tangent line

Answer 1

The average velocity over each time interval can be found using the differentiated function, indefinite integral, area under the curve, or the slope of the tangent line.

Step-by-step explanation:

The average velocity over each time interval can be determined using the following methods:

a) Differentiated function: The average velocity between two time points can be found by calculating the slope of the displacement function between those points. Differentiating the displacement function with respect to time will give you the velocity function. The slope of the velocity function between two time points will give you the average velocity.

b) Indefinite integral: The average velocity can also be found by integrating the velocity function over a time interval and dividing it by the length of the interval.

c) Area under the curve: The displacement function represents the area under the velocity-time graph. Therefore, finding the area under the curve between two time points will give you the average velocity.

d) Slope of the tangent line: The instantaneous velocity at a specific time can be found by calculating the slope of the tangent line to the displacement function at that time.