QuestionAugust 12, 2025

4. A motorboat accelerates uniformly from a velocity of 6.5m/s to the west to a velocity of 1.5m/s to the west. If its acceleration was 2.7m/s^2 to the east, how far did it travel during the acceleration?

4. A motorboat accelerates uniformly from a velocity of 6.5m/s to the west to a velocity of 1.5m/s to the west. If its acceleration was 2.7m/s^2 to the east, how far did it travel during the acceleration?
4. A motorboat accelerates uniformly from a velocity of 6.5m/s to the west to a velocity of 1.5m/s to the west. If its acceleration was 2.7m/s^2 to the east, how far did it travel during the acceleration?

Solution
4.7(195 votes)

Answer

7.41 \, \text{m} Explanation 1. Identify Initial and Final Velocities Initial velocity u = 6.5 \, \text{m/s} (west), final velocity v = 1.5 \, \text{m/s} (west). 2. Determine Acceleration Direction Given acceleration a = 2.7 \, \text{m/s}^2 to the east, which is opposite to the direction of velocities. 3. Use Kinematic Equation for Distance Use **v^2 = u^2 + 2as** where s is the distance traveled. Rearrange to solve for s: s = \frac{v^2 - u^2}{2a}. 4. Substitute Values Substitute v = 1.5 \, \text{m/s}, u = 6.5 \, \text{m/s}, and a = -2.7 \, \text{m/s}^2 (since it's opposite to velocity). s = \frac{(1.5)^2 - (6.5)^2}{2 \times (-2.7)}. 5. Calculate s = \frac{2.25 - 42.25}{-5.4} = \frac{-40}{-5.4} \approx 7.41 \, \text{m}.

Explanation

1. Identify Initial and Final Velocities<br /> Initial velocity $u = 6.5 \, \text{m/s}$ (west), final velocity $v = 1.5 \, \text{m/s}$ (west).<br /><br />2. Determine Acceleration Direction<br /> Given acceleration $a = 2.7 \, \text{m/s}^2$ to the east, which is opposite to the direction of velocities.<br /><br />3. Use Kinematic Equation for Distance<br /> Use **$v^2 = u^2 + 2as$** where $s$ is the distance traveled.<br /> Rearrange to solve for $s$: $s = \frac{v^2 - u^2}{2a}$.<br /><br />4. Substitute Values<br /> Substitute $v = 1.5 \, \text{m/s}$, $u = 6.5 \, \text{m/s}$, and $a = -2.7 \, \text{m/s}^2$ (since it's opposite to velocity).<br /> $s = \frac{(1.5)^2 - (6.5)^2}{2 \times (-2.7)}$.<br /><br />5. Calculate<br /> $s = \frac{2.25 - 42.25}{-5.4} = \frac{-40}{-5.4} \approx 7.41 \, \text{m}$.
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