Question

Two football players move in a straight line directly toward one another. Their equations of motion are as follows:

x₁ = 0.1 m + (-3.1 m/s)t
x₂ = -6.3 m + (2.8 m/s)t
Which player is moving faster?

Answer 1

Player 1 is moving faster with a speed of 3.1 m/s, compared to player 2's speed of 2.8 m/s, since the player with the greater velocity magnitude is the faster one.

Step-by-step explanation:

To determine which football player is moving faster, we need to compare the magnitude of their velocities given by the slope of their equations of motion. The two equations of motion you've provided are:
x₁ = 0.1 m + (-3.1 m/s)t represents player 1,
x₂ = -6.3 m + (2.8 m/s)t represents player 2.

The velocity of each player is the coefficient of the time variable t. For player 1, the velocity is -3.1 m/s, and for player 2, it is 2.8 m/s. By taking the absolute values, we find that player 1's speed is 3.1 m/s, and player 2's speed is 2.8 m/s. Therefore, player 1 is moving faster than player 2 because 3.1 m/s is greater than 2.8 m/s.