An athlete begins at the starting line ( ) of a 100 m straight track that lies on the…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
An athlete begins at the starting line (x=0) of a 100 m straight track that lies on the +x axis. The following timeline describes her motions, all of which occur along the track:
• Segment 1: Sprints 100 m due east in 12 s.
• Segment 2: Rests in place for 3 s.
• Segment 3: Runs 60 m due west in 9 s.
• Segment 4: Walks 40 m due east in 16 s.
Ignore any turning times.
(a) After each individual segment, state the athlete’s position relative to the starting line. Use an algebraic sign to denote direction.
(b) Determine (i) the total distance the athlete travels and (ii) her overall displacement for the entire 40 s interval.
(c) For the full 40 s, evaluate the athlete’s average speed and average velocity, giving numerical values with units and sign where appropriate.
(d) For each motion segment, write an algebraic expression x(t) for the athlete’s position as a function of time measured from the start of that segment. Then construct a qualitative sketch of the complete position-versus-time graph for 0≤t≤40s, clearly indicating key positions and times.