A motorboat accelerates uniformly from a velocity of 6.5 m/s to the west to a velocity of 1.5 m/s to the west. If its acceleration was 2.7 m/s to the est, how far did it travel during the acceleration
Vf^2=Vi^2+2ad
a=2.7 + direction is East, so d will work out to be a negative direction, meaning west.
1.2
To find the distance traveled during the acceleration, we can use the formula:
\[ \text{Distance} = \frac{{\text{Final velocity}^2 - \text{Initial velocity}^2}}{{2 \times \text{Acceleration}}} \]
Given:
Initial velocity (\(v_0\)) = 6.5 m/s (to the west)
Final velocity (\(v\)) = 1.5 m/s (to the west)
Acceleration (\(a\)) = 2.7 m/s\(^{2}\) (to the east)
Plugging the values into the formula, we have:
\[ \text{Distance} = \frac{{(1.5 \, \text{m/s})^2 - (6.5 \, \text{m/s})^2}}{{2 \times 2.7 \, \text{m/s}^2}} \]
\[ \text{Distance} = \frac{{2.25 \, \text{m}^2/\text{s}^2 - 42.25 \, \text{m}^2/\text{s}^2}}{{5.4 \, \text{m/s}^2}} \]
\[ \text{Distance} = \frac{{-40 \, \text{m}^2/\text{s}^2}}{{5.4 \, \text{m/s}^2}} \]
\[ \text{Distance} = -7.4074 \, \text{m} \]
The negative sign indicates that the motorboat traveled in the opposite direction of the acceleration. Therefore, the magnitude of the distance traveled during the acceleration is 7.4074 meters.
To find the distance traveled during the acceleration, we can use the formula:
\[ \text{{Distance}} = \frac{{(\text{{Final Velocity}})^2 - (\text{{Initial Velocity}})^2}}{{2 \times \text{{Acceleration}}}} \]
Given:
Initial velocity (\(v_i\)) = 6.5 m/s to the west
Final velocity (\(v_f\)) = 1.5 m/s to the west
Acceleration (\(a\)) = 2.7 m/s to the west
Now let's substitute the values into the formula:
\[ \text{{Distance}} = \frac{{(1.5 \, \text{{m/s}})^2 - (6.5 \, \text{{m/s}})^2}}{{2 \times 2.7 \, \text{{m/s}}^2}} \]
Calculating this equation will give us the distance traveled during the acceleration.