 The distance, s (in metres), travelled by a child sliding along a flat waterslide after t seconds can be modelled by the function s = 2sqrt3t

The given function modeling the distance \( s \) (in meters) traveled by the child on the waterslide over time \( t \) (in seconds) is:

\[
s = 2\sqrt{3}t
\]

This is a linear function where the distance \( s \) is directly proportional to time \( t \). The coefficient \( 2\sqrt{3} \) represents the constant speed at which the child is sliding.

### Key Points:

1. **Speed Interpretation**: The constant \( 2\sqrt{3} \approx 3.464 \) meters per second is the speed of the child on the waterslide.
2. **Distance Calculation**: For any given time \( t \), you can calculate the distance by multiplying \( t \) with \( 2\sqrt{3} \).
3. **Time Calculation**: For a specific distance, you can find the time by rearranging the equation as \( t = \frac{s}{2\sqrt{3}} \).

### Example Calculations:

1. **Find the distance traveled after 5 seconds**:
   \[
   s = 2\sqrt{3} \times 5 = 10\sqrt{3} \approx 17.32 \text{ meters}
   \]

2. **Find the time to travel 20 meters**:
   \[
   t = \frac{20}{2\sqrt{3}} = \frac{10}{\sqrt{3}} \approx 5.77 \text{ seconds}
   \]

### Additional Questions:

1. What is the distance traveled after 10 seconds?
2. How long will it take for the child to travel 30 meters?
3. If the child slides for 12 seconds, what will be the total distance covered?
4. What would be the speed if the coefficient was \( 3\sqrt{2} \) instead of \( 2\sqrt{3} \)?
5. How would the distance change if the function was \( s = \sqrt{3}t^2 \)?

### Tip:
For any linear distance-time relationship, the coefficient of \( t \) gives the speed directly.

The distance, s (in metres), travelled by a child sliding along a flat waterslide after t seconds can be modelled by the function s = 2sqrt3t.

Explore how to model the distance a child travels on a waterslide using the linear function s = 2√3t. Learn key concepts in algebra, calculate speed and distance over time, and practice example problems. Suitable for students in Grades 6-8.

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