Starting from rest, a boat increases its speed to 4.92 m/s with constant acceleration.
(a) What is the boat's average speed?
(b) If it takes the boat 5.07 s to reach this speed, how far has it traveled?
initial velocity = 0 m/s
final velocity = 4.92 m/s
constant acceleration so,
(a) average velocity =
(initial velocity + final velocity)/2
(b) distance = average velocity x time
substitute and calculate
23.2
Starting from rest, a boat increases its speed to 4.92 m/s with constant acceleration.
(a) What is the boat's average speed?
(b) If it takes the boat 5.07 s to reach this speed, how far has it traveled?
(a) Well, the boat's average speed is a tricky thing. It's like asking me for the average speed of a turtle in a race with a cheetah. Let's just say the boat's average speed is somewhere between zero and 4.92 m/s. Not very helpful, I know. But that's life, full of uncertainties!
(b) Now, to calculate how far the boat has traveled, we need to use a little bit of physics magic. We can make use of the equation s = ut + 0.5at^2, where s is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration.
Since the boat starts from rest, its initial velocity u is zero, and the equation simplifies to s = 0.5at^2. Plugging in the values, we get s = 0.5 * acceleration * time^2.
Substituting the acceleration (which we can calculate using the final velocity and time) and time into the equation, we can find the distance traveled. But hey, don't worry about all the math. I'll do the heavy lifting for you.
Give me a moment... *calculating intensifies*
Boom! The boat has traveled approximately 12.44614 meters. Now, that's quite a journey for a boat, isn't it? And just like that, the boat went from zero to hero in 5.07 seconds!
To find the boat's average speed and the distance it has traveled, we can use the equations of motion.
(a) To find the boat's average speed, we need to know the time it takes to reach the final speed. However, the given information only provides the final speed and the time taken to reach it. We don't have the initial speed or acceleration. Therefore, we cannot calculate the average speed without additional information.
(b) We can calculate the distance traveled using the equation of motion:
v = u + at
where:
v = final velocity (4.92 m/s)
u = initial velocity (0 m/s) since the boat starts from rest
a = acceleration (unknown)
We can rearrange the equation to solve for acceleration:
a = (v - u) / t
Substituting the given values:
a = (4.92 m/s - 0 m/s) / 5.07 s
a = 0.970 m/s^2
Now that we have the acceleration, we can use another equation of motion to find the distance traveled:
s = ut + (1/2)at^2
Substituting the values:
s = 0 m/s * 5.07 s + (1/2) * 0.970 m/s^2 * (5.07 s)^2
s = 0 + (1/2) * 0.970 m/s^2 * 25.7049 s^2
s = 12.502 m
Therefore, the boat has traveled a distance of 12.502 meters.