Question

two drivers narrowly avert a head - on collision. which driver decelerated faster in the first 2.5 seconds since starting to brake? use the two representations, found below, to compare the two relationships.
driver 1

time (seconds)	0	1	2	2.5	3	4	5

(then there is a graph for driver 2 with speed (mph) on the y - axis and time (seconds) on the x - axis. points on the graph include (0, 56), (2.5, 41), and intercepts (-4.83, 0) and (4.83, 0))
answer each question based on the given representations.
what was driver 1’s absolute average rate of deceleration starting at time 0?
what was driver 2’s absolute average rate of deceleration starting at time 0?
which driver decelerated faster?

Explanation:

Step1: Calculate Driver 1's deceleration

The formula for average rate of change (deceleration here) is $\frac{\text{Final Speed} - \text{Initial Speed}}{\text{Final Time} - \text{Initial Time}}$. For Driver 1, initial time $t_1 = 0$ s, initial speed $v_1 = 65$ mph; final time $t_2 = 2.5$ s, final speed $v_2 = 40$ mph. So deceleration $a_1=\frac{40 - 65}{2.5 - 0}=\frac{-25}{2.5}=-10$ mph/s.

Step2: Calculate Driver 2's deceleration

From the graph, at $t = 0$ s, speed $v_1 = 56$ mph; at $t = 2.5$ s, speed $v_2 = 41$ mph. Using the same formula, deceleration $a_2=\frac{41 - 56}{2.5 - 0}=\frac{-15}{2.5}=-6$ mph/s.

Step3: Compare decelerations

The magnitude of deceleration for Driver 1 is $| - 10| = 10$ mph/s, for Driver 2 is $| - 6| = 6$ mph/s. Since $10>6$, Driver 1 decelerated faster.

Answer:

Driver 1 decelerated faster.