Understanding the Scooter's Motion

This problem involves calculating the distance traveled by a scooter under constant acceleration (or deceleration). We are given the initial velocity, the rate at which the velocity changes (acceleration), and the time duration.

Given Information:

• Initial velocity ($u$): 21 m/s
• Acceleration ($a$): The scooter slows down with 50 cm/s². This means the acceleration is in the opposite direction to the velocity. We need to convert this to meters per second squared (m/s²).

  $50 \text{ cm/s}^2 = \frac{50}{100} \text{ m/s}^2 = 0.5 \text{ m/s}^2 $

  Since the scooter is slowing down, the acceleration value used in our calculations will be negative:

  $a = -0.5 \text{ m/s}^2 $

• Time ($t$): 4 s

Calculating Distance Traveled

To find the distance traveled ($s$), we can use the standard kinematic equation:

$s = ut + \frac{1}{2}at^2 $

Let's substitute the given values into the formula:

$s = (21 \text{ m/s}) \times (4 \text{ s}) + \frac{1}{2} \times (-0.5 \text{ m/s}^2) \times (4 \text{ s})^2 $

Step-by-Step Calculation:

1. Calculate the distance covered due to initial velocity:

   $ut = 21 \times 4 = 84 \text{ m} $

2. Calculate the change in distance due to acceleration:

   First, calculate $t^2$: $ (4 \text{ s})^2 = 16 \text{ s}^2 $

   Next, calculate $\frac{1}{2}at^2$: $ \frac{1}{2} \times (-0.5 \text{ m/s}^2) \times (16 \text{ s}^2) $

   $ = -0.25 \times 16 \text{ m} $

   $ = -4 \text{ m} $

   The negative sign indicates that the acceleration opposes the motion, effectively reducing the distance covered compared to if the velocity were constant.
3. Add the two parts to find the total distance:

   $s = 84 \text{ m} + (-4 \text{ m}) $

   $s = 84 \text{ m} - 4 \text{ m} $

   $s = 80 \text{ m} $

Conclusion

After 4 seconds, the scooter has traveled a distance of 80 meters. This matches one of the provided options.