A speedboat increases in speed from 19 m/s
to 31.4 m/s in a distance 193 m.
Find the magnitude of its acceleration.
Answer in units of m/s
To find the magnitude of the acceleration of the speedboat, we can use the formula:
acceleration = change in velocity / time
However, we are only given the initial and final velocities, and not the time taken. In order to find the magnitude of the acceleration, we need to use a different equation that relates velocity, time, and acceleration.
The equation we can use is:
v^2 = u^2 + 2as
Where:
- v is the final velocity (31.4 m/s)
- u is the initial velocity (19 m/s)
- a is the acceleration (which we are trying to find)
- s is the distance traveled (193 m)
Rearranging the equation to solve for acceleration:
a = (v^2 - u^2) / (2s)
Plugging in the values we have:
a = (31.4^2 - 19^2) / (2 * 193)
Calculating the equation:
a = (985.96 - 361) / (386)
a ≈ 0.734 m/s^2
So, the magnitude of the acceleration of the speedboat is approximately 0.734 m/s^2.