A motorboat traveling on a straight course slows down uniformly from 75km/h to 40km/h in a distance of 50m. What is the boat’s acceleration?
To find the boat's acceleration, we can use the formula:
Acceleration (a) = (Final Velocity (v) - Initial Velocity (u)) / Time (t)
In this case, we have the initial velocity (u) as 75 km/h and the final velocity (v) as 40 km/h. However, we do not have the time (t) but we can calculate it using the information provided.
First, let’s convert the velocities from km/h to m/s because the distance provided is in meters.
Initial Velocity (u) = 75 km/h = 75 * (1000 m/3600 s) = 20.83 m/s
Final Velocity (v) = 40 km/h = 40 * (1000 m/3600 s) = 11.11 m/s
Next, we can find the time using the formula:
Distance (d) = (Initial Velocity (u) + Final Velocity (v)) / 2 * Time (t)
We know the distance (d) is 50 meters, so we can rearrange the formula to solve for time:
Time (t) = Distance (d) / ((Initial Velocity (u) + Final Velocity (v)) / 2)
Time (t) = 50 m / ((20.83 m/s + 11.11 m/s) / 2)
Time (t) = 50 m / (31.94 m/s / 2)
Time (t) = 50 m / 15.97 m/s
Time (t) ≈ 3.13 seconds.
Now that we have the time, we can substitute the values into the acceleration formula:
Acceleration (a) = (Final Velocity (v) - Initial Velocity (u)) / Time (t)
Acceleration (a) = (11.11 m/s - 20.83 m/s) / 3.13 s
Acceleration (a) = -9.72 m/s / 3.13 s
Acceleration (a) ≈ -3.11 m/s²
Therefore, the boat’s acceleration is approximately -3.11 m/s². The negative sign indicates that the boat is slowing down.