Let's solve the problem step-by-step.
Step 1: Convert the speeds from km/h to m/s
Given:
- Initial speed: [tex]\(18 \, \text{km/h}\)[/tex]
- Final speed: [tex]\(36 \, \text{km/h}\)[/tex]
To convert from km/h to m/s, use the conversion factor: [tex]\(1 \, \text{km/h} = \frac{1}{3.6} \, \text{m/s}\)[/tex].
So, for the initial speed:
[tex]\[18 \, \text{km/h} = 18 \times \frac{1}{3.6} \, \text{m/s} = 5 \, \text{m/s}\][/tex]
For the final speed:
[tex]\[36 \, \text{km/h} = 36 \times \frac{1}{3.6} \, \text{m/s} = 10 \, \text{m/s}\][/tex]
Step 2: Calculate the change in speed
Change in speed (Δv) = Final speed - Initial speed
[tex]\[Δv = 10 \, \text{m/s} - 5 \, \text{m/s} = 5 \, \text{m/s}\][/tex]
Step 3: Calculate the acceleration
Acceleration [tex]\(a\)[/tex] is defined as the change in speed divided by the time taken.
Given:
- Change in speed [tex]\(Δv = 5 \, \text{m/s}\)[/tex]
- Time [tex]\(t = 5 \, \text{s}\)[/tex]
So, acceleration [tex]\(a\)[/tex] is:
[tex]\[a = \frac{Δv}{t} = \frac{5 \, \text{m/s}}{5 \, \text{s}} = 1 \, \text{m/s}^2\][/tex]
Conclusion:
The acceleration of the automobile is [tex]\(1 \, \text{m/s}^2\)[/tex].
Therefore, the correct answer is:
a. [tex]\(1 \, \text{m/s}^2\)[/tex]
