Answer :
To find the rate of acceleration, we can use the kinematic equation that relates initial velocity u, final velocity v, acceleration a, and distance s:
[tex]v^2=u^2+2as[/tex]
Given:
- Initial velocity, u = 5.5 m/s
- Final velocity, v = 9.0 m/s
- Distance, s = 32 m
We need to solve for acceleration a. Rearranging the equation for a:
[tex]a=(v^2-u^2)/2s[/tex]
Substituting the given values:
[tex]\[ a = \frac{(9.0 \, \text{m/s})^2 - (5.5 \, \text{m/s})^2}{2 \times 32 \, \text{m}} \][/tex]
Let's calculate it:
[tex]\[ a = \frac{81 - 30.25}{64} \]\[ a = \frac{50.75}{64} \]\[ a \approx 0.793 \, \text{m/s}^2 \][/tex]
So, the rate at which the boat is accelerating is approximately [tex]\( 0.793 \, \text{m/s}^2 \).[/tex]
