To calculate the time it takes for the boat to accelerate, we can use the following kinematic equation:
v² = u² + 2as
where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
Given:
u = 5 m/s
v = unknown (since we want to find the time of acceleration, not the final velocity)
a = I m/s (where I is the acceleration in integer form)
s = 40 m
Rearranging the equation, we get:
v² = u² + 2as
v² = (5 m/s)² + 2(I m/s²)(40 m)
v² = 25 m²/s² + 80I m²/s²
v² = 25 m²/s² + 80I m²/s²
Since the boat starts from rest (u = 0), the equation simplifies to:
v² = 80I m²/s²
To find the time, we need to solve for v. Taking the square root of both sides of the equation:
v = √(80I) m/s
Now, we know that v = u + at, where t is the time of acceleration. Since the initial velocity is 0 (u = 0), we can simplify the equation:
√(80I) m/s = a(t)
Rearranging the equation to solve for t:
t = √(80I) / a
Now, you mentioned that the acceleration is "Im/s," but I assume that you meant "I m/s²" (meters per second squared) for consistency with the standard unit of acceleration. With this assumption, we can calculate the time of acceleration.
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Answer:
To calculate the time it takes for the boat to accelerate, we can use the following kinematic equation:
v² = u² + 2as
where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
Given:
u = 5 m/s
v = unknown (since we want to find the time of acceleration, not the final velocity)
a = I m/s (where I is the acceleration in integer form)
s = 40 m
Rearranging the equation, we get:
v² = u² + 2as
v² = (5 m/s)² + 2(I m/s²)(40 m)
v² = 25 m²/s² + 80I m²/s²
v² = 25 m²/s² + 80I m²/s²
Since the boat starts from rest (u = 0), the equation simplifies to:
v² = 80I m²/s²
To find the time, we need to solve for v. Taking the square root of both sides of the equation:
v = √(80I) m/s
Now, we know that v = u + at, where t is the time of acceleration. Since the initial velocity is 0 (u = 0), we can simplify the equation:
√(80I) m/s = a(t)
Rearranging the equation to solve for t:
t = √(80I) / a
Now, you mentioned that the acceleration is "Im/s," but I assume that you meant "I m/s²" (meters per second squared) for consistency with the standard unit of acceleration. With this assumption, we can calculate the time of acceleration.