Where will a bicyclist be when achieving a velocity of 10.0 m/s, if initially 2.0 m away and accelerating at 1.2 m/s²?

To determine the position of the bicyclist when achieving a velocity of 10.0 m/s, we can use the equations of motion. The key to solving this problem is recognizing that the bicyclist starts with an initial position and then accelerates to reach the desired velocity.

1. We start with the initial conditions:

• Initial position (displacement): ( x_0 = 2.0 ) m

• Initial velocity: ( v_0 = 0 ) m/s (since the context suggests starting from rest or not provided)

• Final velocity: ( v = 10.0 ) m/s

• Acceleration: ( a = 1.2 ) m/s²

2. We can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:

[

v^2 = v_0^2 + 2a(x - x_0)

]

Substituting in the known values:

[

(10.0)^2 = (0)^2 + 2(1.2)(x - 2.0)

]

This simplifies to:

[