... Starting from rest, a boat increases its speed to 4.82 m / s with constant acceleration. (a)

... Starting from rest, a boat increases its speed to 4.82 m...

... Starting from rest, a boat increases its speed to 4.82 $\mathrm{m} / \mathrm{s}$ with
constant acceleration. (a) What is the boat's average speed? (b) If
it takes the boat 4.77 s to reach this speed, how far has it traveled?

Key Concepts

Uniformly Accelerated Motion

Uniformly accelerated motion describes motion where the acceleration remains constant over time. This concept is fundamental in kinematics as it allows the use of standard equations to correlate initial speed, final speed, time, and displacement, making it possible to predict an object's future state if its acceleration parameter is known.

Average Speed

Average speed is the total distance traveled divided by the time taken. In scenarios involving constant acceleration from rest, the average speed can be conveniently calculated as half the final speed because the speed increases uniformly over time.

Kinematic Equations

Kinematic equations are formulas that describe the relationships between displacement, velocity, acceleration, and time in cases of constant acceleration. These equations are essential tools in solving motion problems, enabling one to determine unknown quantities based on known initial conditions and physical constraints.

Transcript

00:01 Okay, in this problem we have a boat that increase its speed to, let's see, final velocity of 4 .82 meters per second.

00:14 We know that he begins at rest, so his initial velocity is 0 meters per second.

00:22 And the first item of the problem, we want to know what is the average velocity.

00:30 Velocity of the boat.

00:33 Okay, well the problem says that he has constant acceleration.

00:38 This is really important because when we have constant acceleration, we just need to calculate the average velocity, we just need to do this equation.

00:51 One half of the initial velocity plus the final velocity.

00:56 So the average velocity of the boat is going to be one half of zero plus 4 .82.

01:09 This is equal to 2 .41 meters per second.

01:17 This is the answer to the first item.

01:21 The second item, we want to find out, let's see, we want to find out what is the distance the boat travel.

01:33 So we want to know the displacement of the boat, knowing that he will spend the time of 4 .77 seconds to complete his movement.

01:46 Okay, well, we know the velocities.

01:51 The first thing we find out.

01:54 And we want to know what is the displacement.

01:57 So the only equation that we know that involves velocity with the speed, displacement is just v square equals to v0 square plus 2 times a times the displacement.

02:12 Okay, so this is a zero.

02:15 Okay, so we have a zero, yes, we have the final velocity...

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