Question

A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t)=50.0 cm+(2.00 cm/s)t−(0.0625 cm/s²)t². At what time t is the turtle second time a distance of 10.0 cm from its starting point?

Answer 1

To find the time at which the turtle is 10.0 cm from its starting point for the second time, we need to solve a quadratic equation. The solution to the equation is t = 10.0 s.

Step-by-step explanation:

The turtle's position as a function of time is given by the equation x(t) = 50.0 cm + (2.00 cm/s)t - (0.0625 cm/s²)t². To find the time at which the turtle is 10.0 cm from its starting point for the second time, we need to solve the equation 10.0 cm = 50.0 cm + (2.00 cm/s)t - (0.0625 cm/s²)t².

This equation can be rearranged to a quadratic equation in the form at² + bt + c = 0, where a = -0.0625 cm/s², b = 2.00 cm/s, and c = 40.0 cm. We can then use the quadratic formula to solve for t, which gives us two solutions: t = 2.0 s and t = 10.0 s.

However, since we are looking for the second time the turtle is 10.0 cm from its starting point, we can discard the first solution and conclude that the turtle is 10.0 cm from its starting point for the second time at t = 10.0 s.