Answer:
To find the distance the book would cover in 1.5 seconds, we can use the equation for distance covered by an object under constant acceleration:
\[d = v_i t + \frac{1}{2} a t^2\]
Where:
- \(d\) is the distance covered,
- \(v_i\) is the initial velocity (2 m/s downwards in this case),
- \(a\) is the acceleration (in this case, due to gravity, \(a = 9.81\) m/s² downwards), and
- \(t\) is the time (1.5 seconds).
Plugging in the values:
\[d = (2 \, \text{m/s} \times 1.5 \, \text{s}) + \frac{1}{2} \times (-9.81 \, \text{m/s}^2) \times (1.5 \, \text{s})^2\]
\[d = 3 \, \text{m} - \frac{1}{2} \times 9.81 \, \text{m/s}^2 \times 2.25 \, \text{s}^2\]
\[d = 3 \, \text{m} - 11.035 \, \text{m}\]
\[d \approx -8.035 \, \text{m}\]
The negative sign indicates that the direction is downwards. So, the book would cover approximately 8.035 meters downwards in 1.5 seconds.
