Question

At what time t , for , 0 < x < 2is the line tangent to the path of the car parallel to the -axis? give a reason for your answer.

a. t = 0
b. t = 1
c. t= 2
d. t = 1/2

Answer 1

The line is tangent to the path of the car parallel to the y-axis at t = 1.

Step-by-step explanation:

To find the time at which the line is tangent to the path of the car parallel to the y-axis, we need to find the time when the slope of the path equation is equal to the slope of the line.

The slope of the line is 2.0 km/min, so we need to find the time when the slope of the path equation is also 2.0 km/min. The path equation is given as y = (2.0 km/min) x + 0. Setting the derivative of y with respect to x equal to 2.0 km/min, we have 2.0 = 2.0 km/min. Solving for x, we find that x = 1.

Therefore, the line is tangent to the path of the car parallel to the y-axis at t = 1.