Question

a = \frac{v_f - v_i}{t}
final velocity (m/s)
initial velocity (m/s)
v_f - v_i (\delta v)
time (s)
a = \frac{\delta v}{t}
26 m/s
20 m/s
6
5 m/s
15 m/s
5
compare and contrast positive and negative acceleration.

Explanation:

Step1: Calculate $\Delta v$ for first - row

$\Delta v=v_f - v_i=26 - 20=6$ m/s. Then $a=\frac{\Delta v}{t}=\frac{6}{6}=1$ m/s².

Step2: Calculate $\Delta v$ for second - row

$\Delta v=v_f - v_i=5 - 15=- 10$ m/s. Then $a=\frac{\Delta v}{t}=\frac{-10}{5}=-2$ m/s².

Step3: Compare positive and negative acceleration

Positive acceleration ($a = 1$ m/s² in first case) means an object is speeding up (since final velocity is greater than initial velocity). Negative acceleration ($a=-2$ m/s² in second case) means an object is slowing down (since final velocity is less than initial velocity).

Answer:

Final velocity (m/s)	Initial velocity (m/s)	$v_f - v_i$ ($\Delta v$) (m/s)	Time (s)	$a=\frac{\Delta v}{t}$ (m/s²)
5	15	- 10	5	- 2

Positive acceleration indicates speeding up, negative acceleration indicates slowing down.