n boat starts from rest and accelerates at a constant rate to a final speed of 28 m/s over a distance of 780 m. How much time will this take?
Vf^2=Vi^2+2ad
solve for a, then..
28=at solve for t.
actually, there is an easier way. Avg velocity is 14m/s
time to travel= distance/avgvelocity
To find the time it takes for the boat to accelerate to its final speed, you can use the equation of motion:
v = u + at
Where:
v = final velocity (28 m/s)
u = initial velocity (0 m/s, since the boat starts from rest)
a = acceleration
t = time taken
Since the boat accelerates at a constant rate, the acceleration (a) remains the same throughout the entire distance.
Now, we need to find the acceleration using the following equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (28 m/s)
u = initial velocity (0 m/s)
a = acceleration
s = distance (780 m)
Plugging in the values:
(28 m/s)^2 = (0 m/s)^2 + 2a(780 m)
784 m^2/s^2 = 2a(780 m)
Divide both sides by 2(780 m):
392 m/s^2 = a
Now that we know the acceleration, we can go back to the first equation:
v = u + at
Plugging in the values:
28 m/s = 0 m/s + (392 m/s^2)t
Rearranging the equation to solve for t:
t = (28 m/s) / (392 m/s^2)
t = 0.0714 seconds
Therefore, it will take approximately 0.0714 seconds for the boat to accelerate from rest to its final speed of 28 m/s over a distance of 780 m.