In the diagram of a ball falling toward Earth in a vacuum, using the relation change in $v = 9.8\,\text{m/s}^2 \times t$, what is the ball’s velocity after 2 seconds? (A) 39.2 (B) 19.6 (C) 9.8 (D) 29.4

What the given formula is telling you

In a vacuum, the ball’s acceleration is (approximately) constant at $g = 9.8\,\text{m/s}^2$, so its velocity changes by the same amount every second.

Plug in the time $t = 2\,\text{s}$

The problem gives:

$$\Delta v = 9.8\,\text{m/s}^2 \times t$$

Substitute $t = 2$:

$$\Delta v = 9.8\times 2 = 19.6\,\text{m/s}$$

So after 2 seconds, the ball’s speed is $19.6\,\text{m/s}$ (directed downward).

Match to the multiple-choice options

Option B matches the value $19.6$ (even though the options incorrectly write units as $\text{m/s}^2$; velocity should be in $\text{m/s}$).