Acceleration Calculation for a Changing Speed

This problem asks us to find the acceleration of a car when its speed changes over a specific period. Acceleration is the rate at which an object's velocity changes over time.

Understanding the Variables

• Initial Speed (\(u\)): The speed the car starts with. Here, \(u = 40\) m/s.
• Final Speed (\(v\)): The speed the car ends with. Here, \(v = 20\) m/s.
• Time (\(t\)): The duration over which the speed changes. Here, \(t = 5\) s.
• Acceleration (\(a\)): The value we need to find.

Formula for Acceleration

Acceleration is calculated using the formula:

\( a = \frac{v - u}{t} \)

Where:

• \(a\) is acceleration
• \(v\) is the final velocity
• \(u\) is the initial velocity
• \(t\) is the time interval

Step-by-Step Calculation

1. Identify the given values:
   • Initial speed, \(u = 40\) m/s
   • Final speed, \(v = 20\) m/s
   • Time, \(t = 5\) s
2. Substitute the values into the acceleration formula:

   \( a = \frac{20 \text{ m/s} - 40 \text{ m/s}}{5 \text{ s}} \)

3. Calculate the change in speed:

   \( v - u = 20 - 40 = -20 \text{ m/s} \)

   The negative sign indicates that the speed is decreasing.

4. Divide the change in speed by the time taken:

   \( a = \frac{-20 \text{ m/s}}{5 \text{ s}} \)

5. Determine the final acceleration value:

   \( a = -4 \text{ m/s}^2 \)

Conclusion

The acceleration of the car is \( -4 \text{ m/s}^2 \). The negative sign signifies that the car is decelerating or slowing down.