A player is standing 12 meters to the right of a lamppost. He starts to walk with a constant acceleration of 2 m/s2 towards the lamppost. After 6 seconds, how far will the player be from the lamppost in meters?
To find the distance the player will be from the lamppost after 6 seconds, we can use the kinematic equation:
Displacement (d) = Initial position (x0) + Initial velocity (v0) * time (t) + (1/2) * acceleration (a) * time squared (t^2)
In this case, the player's initial position (x0) is 12 meters to the right of the lamppost, so x0 = 12 meters. The initial velocity (v0) is 0 m/s since the player starts from rest, and the acceleration (a) is 2 m/s^2.
Plugging these values into the equation, we get:
d = x0 + v0 * t + (1/2) * a * t^2
d = 12 + 0 * 6 + (1/2) * 2 * 6^2
d = 12 + 0 + (1/2) * 2 * 36
d = 12 + 0 + 1 * 36
d = 12 + 0 + 36
d = 48 meters
Therefore, the player will be 48 meters away from the lamppost after 6 seconds.