Question

A boat travels 12.0 m [E] while its speed changes from from 9.50 m/s to 5.50 m/s. What is the boat’s acceleration (in m/s²)? How long (in s) does it take the boat to go through that speed change? Show your work and steps.

Answer 1

To find the boat's acceleration and the time it takes to go through the speed change, we can use the following equations of motion:

1. Average Velocity (v_avg) = (v_initial + v_final) / 2
2. Acceleration (a) = (v_final - v_initial) / t

Given: Initial velocity (v_initial) = 9.50 m/s Final velocity (v_final) = 5.50 m/s Displacement (d) = 12.0 m We need to find the acceleration (a) and time (t).

First, we can calculate the average velocity: v_avg = (v_initial + v_final) / 2 v_avg = (9.50 m/s + 5.50 m/s) / 2 v_avg = 7.50 m/s

Next, we can use the formula for average velocity to find the time taken (t) using the given displacement: v_avg = d / t 7.50 m/s = 12.0 m / t

Now we can solve for t: t = d / v_avg t = 12.0 m / 7.50 m/s t ≈ 1.60 s

Finally, we can calculate the acceleration (a): a = (v_final - v_initial) / t a = (5.50 m/s - 9.50 m/s) / 1.60 s a = -4.00 m/s / 1.60 s a ≈ -2.50 m/s²

Therefore, the boat's acceleration is approximately -2.50 m/s², and it takes approximately 1.60 seconds for the boat to go through the speed change. The negative sign indicates that the boat is decelerating or slowing down.