Question

starting from home, tom walks to his friend’s house and then stays there for a while. when he realizes he’s late for dinner, he runs home quickly.
x = the time that has passed.
y = toms distance from home.
a
b
c
d

Explanation:

Step1: Analyze Tom's movement phases

Tom starts at home (distance \( y = 0 \) when \( x = 0 \)). First, he walks to his friend's house: distance from home increases with time (linear, since walking speed is constant). Then he stays: distance remains constant (horizontal line). Then he runs home: distance decreases to 0, and since he runs (faster than walking), the slope of the decreasing part is steeper in magnitude than the increasing part (but since it's decreasing, the slope is negative, but we look at the rate of change).

Step2: Evaluate each graph

• Graph A: Discrete points, not a continuous graph of distance vs time. Eliminate.
• Graph B: Distance only increases, no staying or returning. Eliminate.
• Graph C: Starts at (0,0), increases (walking to friend's), flat (staying), then decreases to 0 (running home). Matches the movement.
• Graph D: Distance increases non - linearly, no staying or returning. Eliminate.

Answer:

C