An iceboat has a constant velocity toward the east when a...

An iceboat has a constant velocity toward the east when a sudden gust of wind causes the icchoat to have a constant acceleration toward the east for a period of $3.0 \mathrm{~s}$. A plot of $x$ versus $t$ is shown in Fig. $2-47,$ where $t=0$ is taken to be the instant the wind starts to blow and the positive $x$ axis is toward the east. (a) What is the acceleration of the iceboat during the $3.0 \mathrm{~s}$ interval? (b) What is the velocity of the iccboat at the cnd of the $3.0 \mathrm{~s}$ interval? (c) If the acceleration remains constant for an additional $3.0 \mathrm{~s}$, how far does the iccboat travel during this second $3.0 \mathrm{~s}$ interval?

Key Concepts

Constant Acceleration

This concept refers to a situation where an object’s acceleration remains the same throughout the motion. Under constant acceleration, the change in velocity is uniform over equal intervals of time, which simplifies the analysis of the object's motion using specific kinematic equations.

Kinematic Equations for Uniformly Accelerated Motion

These equations relate displacement, initial velocity, final velocity, acceleration, and time. They are fundamental tools in solving problems involving constant acceleration, allowing prediction of an object's future position or speed based on its current state and applied acceleration.

Displacement-Time Graph Analysis

A displacement versus time graph can reveal key aspects of motion such as speed, acceleration, and the overall behavior of an object. In cases of constant velocity, the graph is linear, while a changing slope indicates acceleration. The curvature of such graphs helps in visualizing and quantifying the motion parameters.

Time Interval Analysis

Breaking down the motion into specific time intervals allows for a step-by-step understanding of how constant acceleration impacts motion over discrete periods. This involves calculating changes in displacement and velocity over each interval, which is particularly useful when analyzing sequential phases of motion with uniform acceleration.

Transcript

00:01 In this problem of motion along a straight line we have given that an ice boat has a constant velocity towards the east when a sudden gust of wind causes the ice to have a constant acceleration towards east.

00:17 So let's suppose this is the boat and this is moving towards east.

00:21 When a sudden gust of wind appears it has to accelerate that means wind is applying certain force on that boat.

00:30 For a period of 3 seconds and acceleration is for 3 seconds and a plot of x versus time t is shown i'm showing you so this is the figure for that where t is equal to 0 say this is is time t is equal to 0 is taken to be instant the wind instant the wind starts to blow and positive x x x xx towards the east so this is the positive x xx towards the east we have to find what is the acceleration of iceboat during 3 second interval? so we have to find the acceleration of the iceboat during 3 seconds of interval.

01:13 So we have to pick 2 points on this graph.

01:16 So let's suppose the first point is say t is equal to 2 seconds, say this is t is equal to 2 seconds and position it as say this is 16 meters and t is equal to 3 second this is at this is 27 meters and now we have to apply the formula that is x1 is equal to or we can say this is x is equal to this is a constant velocity so this is v0 multiplied with t plus half and acceleration and t square now x1 putting the value x1 which is equals to 16 so v0 is constant so v0 and t is equal to 2 plus half and acceleration is a and t is equal to 2 square say this is equation number 1.

02:01 And x1 is equals to here 16 now putting the value second say this value would be 27 and v0 multiplied with 3 plus half acceleration and this is 3 square so this is equation number 2 now by solving first and second we get initial velocity is equals to 6 .0 meters per second and acceleration comes to be 2 .0 meters per second square so this is the answer of a part a that is acceleration is equal to 2 meters per second square.

02:39 Now part b, part b says what is the velocity of iceboat at the end of 3 seconds...

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