To find the final speed of the car, we can use the following kinematic equation:

$v_f = v_i + a \cdot t$

Where:

• $v_f$ is the final speed (in m/s),
• $v_i$ is the initial speed (in m/s),
• $a$ is the acceleration (in m/s²),
• $t$ is the time (in seconds).

Step 1: Convert initial speed to m/s

The initial speed of the car is given in km/h, so we need to convert it to m/s:

$v_i = 80 \, \text{km/h} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = 22.22 \, \text{m/s}$

Step 2: Apply the kinematic equation

Now, substitute the values into the equation: $v_f = 22.22 \, \text{m/s} + 5 \, \text{m/s²} \times 10 \, \text{s}$

$v_f = 22.22 \, \text{m/s} + 50 \, \text{m/s} = 72.22 \, \text{m/s}$

Thus, the car's final speed after accelerating for 10 seconds is 72.22 m/s.

Would you like further details or have any questions?

Related Questions:

1. What is the total distance traveled during the acceleration?
2. How would the final speed change if the acceleration was 3 m/s²?
3. What would the final speed be if the car accelerated for 5 seconds instead of 10?
4. How long would it take the car to double its initial speed at this acceleration?
5. What is the car's kinetic energy before and after the acceleration?

Tip:

Always convert units to the same system (e.g., m/s for speed and m/s² for acceleration) before solving problems to avoid errors.