Question

The positions of an object moving in a straight line is given by s = 2t² where s is in the meters and t is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 19 meters?

Answer 1

To calculate the time it takes for an object to move 19 meters based on the given position-time equation (s = 2t²), we solve for t by substituting 19 for s, dividing by 2, and taking the square root of the result, which yields approximately 3.1 seconds (to the nearest tenth).

Step-by-step explanation:

The student is asking how to find the time it takes for an object to move 19 meters when its position over time is given by the equation s = 2t², where s represents the position in meters and t is the time in seconds. To find the time when s is 19 meters, we set up and solve the equation for t.

• First, we substitute 19 for s in the equation: 19 = 2t².
• Then, we solve for t² by dividing both sides by 2: t² = 19/2.
• Finally, we take the square root of both sides to find t: t = √(19/2).

Calculating this, we find that t ≈ 3.1 seconds (to the nearest tenth).