A speedboat increases its speed uniformly from v1 = 20 m/s to vf = 26 m/s in a distance of 1.60 102 m.
Substitute given values, obtaining the acceleration.
Find the time it takes the boat to travel the given distance.
Vf^2 = Vo + 2ad,
a = (Vf^2 - Vo^2) / 2d,
a = ((26)^2 - (24)^2) / 320 = 0.8625.
Vf = Vo + at,
t = (Vf - Vo) / a,
t = (26 - 20) / 0.6625 = 6.96s.
To find the acceleration, we can use the formula:
\(a = \frac{{vf - v1}}{{d}}\)
where:
a = acceleration
vf = final velocity
v1 = initial velocity
d = distance
Substituting the given values:
\(a = \frac{{26 \, \text{m/s} - 20 \, \text{m/s}}}{{1.60 \times 10^2 \, \text{m}}}\)
Simplifying:
\(a = \frac{{6 \, \text{m/s}}}{{1.60 \times 10^2 \, \text{m}}}\)
To find the time it takes the boat to travel the given distance, we can use the formula:
\(t = \frac{{d}}{{v1}}\)
Substituting the given values:
\(t = \frac{{1.60 \times 10^2 \, \text{m}}}{{20 \, \text{m/s}}}\)
Simplifying:
\(t = 8 \, \text{s}\)
Therefore, the acceleration is \(3.75 \times 10^{-2} \, \text{m/s}^2\) and it takes 8 seconds for the boat to travel the given distance.
To find the acceleration, we can use the formula for uniformly accelerated motion:
vf^2 = v1^2 + 2aΔx
where:
vf is the final velocity (26 m/s)
v1 is the initial velocity (20 m/s)
a is the acceleration
Δx is the change in distance (1.60 * 10^2 m)
Substituting the given values into the equation:
(26 m/s)^2 = (20 m/s)^2 + 2a(1.60 * 10^2 m)
676 m^2/s^2 = 400 m^2/s^2 + 320a m
Subtracting 400 m^2/s^2 from both sides:
276 m^2/s^2 = 320a m
Now, to find the acceleration (a), we can rearrange the equation:
a = (276 m^2/s^2) / (320 m) ≈ 0.8625 m/s^2
To find the time it takes the boat to travel the given distance, we can use the formula:
vf = v1 + at
where:
vf is the final velocity (26 m/s)
v1 is the initial velocity (20 m/s)
a is the acceleration (0.8625 m/s^2)
t is the time
Substituting the given values into the equation:
26 m/s = 20 m/s + (0.8625 m/s^2)t
Subtracting 20 m/s from both sides:
6 m/s = (0.8625 m/s^2)t
Now, we can solve for t:
t = (6 m/s) / (0.8625 m/s^2) ≈ 6.95 s
Therefore, it takes the speedboat approximately 6.95 seconds to travel the given distance.