Sam is taking his girlfriend Sally out for a ride in his boat. He starts out at rest. He accelerates with an acceleration of 0.263 m/s^2 for 92.1 s. At that time Sally decides they are going fast enough and the boat moves at constant speed for a distance of 286 m. Then Sally decides she want to go a little faster and they accelerate at 0.197 m/s^2 for another 45.1s.
Total displacement of boat = 2690m
A)What is the final velocity of the boat?
B)What is the total time the boat moves?
A) To find the final velocity of the boat, we can use the equation for constant acceleration:
vf = vi + at
where:
vf is the final velocity,
vi is the initial velocity,
a is the acceleration, and
t is the time.
In this case, the boat starts from rest, so the initial velocity (vi) is 0. The acceleration (a) is given as 0.263 m/s^2, and the time (t) is 92.1 s.
Plugging in the values:
vf = 0 + (0.263 m/s^2) * (92.1 s)
vf = 24.1983 m/s
So, the final velocity of the boat is 24.1983 m/s.
B) To find the total time the boat moves, we need to sum up the individual times of acceleration and constant speed.
The time for constant acceleration (t1) is given as 92.1 s.
The time for constant speed (t2) is given as 45.1 s.
The total time (t_total) is the sum of t1 and t2:
t_total = t1 + t2
t_total = 92.1 s + 45.1 s
t_total = 137.2 s
So, the total time the boat moves is 137.2 seconds.