To figure out acceleration from velocity and time in a straight line, we need to understand how these three ideas connect.

• Acceleration (a) tells us how fast something is speeding up or slowing down. We can find it by looking at the change in velocity (v) over a certain period of time (t).

This can be shown with this formula:

$a = \frac{\Delta v}{\Delta t}$

Here, $\Delta v$ is the change in velocity, and $\Delta t$ is the change in time.

• To find the change in velocity, we subtract the starting velocity ($v_i$) from the ending velocity ($v_f$):

$\Delta v = v_f - v_i$

• For time, we look at the difference between the time it started ($t_i$) and the time it ended ($t_f$):

$\Delta t = t_f - t_i$

Putting everything together, we can calculate acceleration like this:

$a = \frac{(v_f - v_i)}{(t_f - t_i)}$

This formula shows that acceleration depends on how much the velocity changes and the time it takes for that change.

When you're calculating acceleration in real life, it's important to use the same units. For example, make sure the velocity is in meters per second (m/s) and time is in seconds (s). This way, you’ll get the acceleration in the correct units, typically meters per second squared (m/s²).

• Example: Let’s say a car goes from 10 m/s to 30 m/s in 5 seconds. We can find the acceleration like this:

$a = \frac{30 \, \text{m/s} - 10 \, \text{m/s}}{5 \, \text{s}} = \frac{20 \, \text{m/s}}{5 \, \text{s}} = 4 \, \text{m/s}^2$

This tells us that the car speeds up by 4 m/s every second, which helps us understand how things move in a straight line.