Question

what is true about the motion of the cyclists based on the graph? check all that apply consider the position vs. time graphs below for cyclists a and b. cyclist a has a greater velocity cyclist b has a greater velocity cyclist a has a further position at 3 seconds cyclist b has a further position at 3 seconds cyclist a has a further position at 8 seconds cyclist b has a further position at 8 seconds both cyclists are in dynamic equilibrium because the velocity is constant both cyclists are in static equilibrium because the forces are balanced the cyclists have the same position at 5 seconds

Explanation:

Step1: Recall velocity - position - time relation

Velocity is slope of position - time graph. Steeper slope means greater velocity. Slope of A is steeper than B, so cyclist A has a greater velocity.

Step2: Check positions at specific times

At \(t = 3\) s, cyclist B is further as B's graph has higher \(x\) - value. At \(t=8\) s, cyclist A is further as A's graph has higher \(x\) - value.

Step3: Analyze equilibrium

Since velocity is constant (straight - line graphs), both cyclists are in dynamic equilibrium. Static equilibrium means no motion, which is not the case here.

Step4: Identify intersection point

The two graphs intersect at \(t = 5\) s, so they have the same position at 5 seconds.

Answer:

Cyclist A has a greater velocity
Cyclist B has a further position at 3 seconds
Cyclist A has a further position at 8 seconds
Both cyclists are in dynamic equilibrium because the velocity is constant
The cyclists have the same position at 5 seconds