A cyclist increases her speed from 6 m/s to 12 m/s in 3 seconds on a straight road. What is her acceleration during this period?

The correct option is 2 m/s².

Understanding Acceleration:
Acceleration is defined as the rate of change of velocity with respect to time. When an object moving in a straight line changes its speed, its acceleration can be calculated using the formula:

$$a=\frac{v-u}{t}$$

Where:
• $a$ is the acceleration,
• $v$ is the final velocity,
• $u$ is the initial velocity, and
• $t$ is the time duration of the change.

Step-by-Step Calculation:
1. Identify the given values from the problem statement:
Initial velocity,
$u=6\text{m/s}$
Final velocity,
$v=12\text{m/s}$
Time period,
$t=3\text{s}$
2. Calculate the change in velocity:
$\Delta v=v-u=12\text{m/s}-6\text{m/s}=6\text{m/s}$
3. Substitute these values into the acceleration formula:
$a=\frac{6\text{m/s}}{3\text{s}}=2{\text{m/s}}^2$
Therefore, the cyclist's acceleration during this period is indeed 2 m/s².