In Problem 71, let the height h equal 6.00 m and the speed vboy equal 2.00 m / s . Assume that

In Problem 71, let the height h equal 6.00 m and the speed...

Key Concepts

Speed-Time Graph

A speed-time graph is a graphical representation of how an object’s speed changes over time. It is used to visualize motion by plotting speed on the vertical axis against time on the horizontal axis. For motions with constant acceleration, the graph is a straight line, whereas for varying acceleration, the graph may be curved. This type of graph provides insight into how acceleration, deceleration, or periods of constant speed occur during motion.

Acceleration-Time Graph

An acceleration-time graph shows how an object’s acceleration varies with time. By plotting constant or changing acceleration values on the vertical axis against time on the horizontal axis, one can identify whether the acceleration remains constant or fluctuates during the motion. The area under the acceleration-time curve represents the change in velocity, linking this graph directly to the speed-time graph.

Uniform Acceleration

Uniform acceleration refers to the scenario where an object's acceleration is constant over time. This concept is central in kinematics because it simplifies the analysis and equations of motion. When acceleration is constant, the speed-time graph appears as a straight line, and standard kinematic equations can be directly applied to determine velocity, displacement, and other motion characteristics.

Data Tabulation and Graphical Analysis

Data tabulation involves recording discrete values of kinematic quantities such as speed and acceleration at specific time intervals. This systematic approach is crucial for accurately constructing graphical representations of motion. Graphical analysis, on the other hand, uses these tabulated data points to create visual plots that help in understanding trends, behaviors, and key features of the motion under study.

Transcript

00:01 Hello everyone here it is given a boy is pulling the food pack as shown in the figure if h to be equal to 6 meter and velocity of y is 2 meter per second and speed of food pack initial speed of food pack is zero we have to calculate we have to tabulate and plot the graph sorry tabulate and graph speed be tabulate and plot 80 graph range of time is 0 to 5 second with interval of 0 .5 second let us start solving it speed of the y is defined as d x upon d t speed of food pack is defined as d x upon d t into sine of theta that is velocity of y into sine of theta which can be also written as velocity of y into x upon n or may be also written as x will be length of this part so by using pythal grostrum you may write x square plus h square and acceleration of the footpeck will be dv upon d t so it may be written as h square upon velocity square of y divided by x square plus h square to the power three by two since h is given six meter y speed is given two meter per second velocity of foot pack is written so x will be equal velocity of y into time since v skull to b square y into t upon b square y into t plus h square k power half so you may write 4 t upon 4 t square plus 4 t square plus 36 k power half t and velocity graph you can so you can tablet now t measured in second velocity.

04:23 Keep on putting the value in a relation.

04:26 Zero time starting with zero.

04:32 It will be 0 .5 .3.

04:38 You are measuring in meter per second.

04:41 Time you are measuring in second.

04:43 1 second .6 .1 .5 .892.

04:54 1 .11 2 .5 1 .28 3 1 .41 3 .5 1 .5 1 .5 to 4 .6 4 .5 1 .6 .6.

05:32 1 .7 1.

05:40 Now using these value we have to plot the graph velocity on the y -axis.

06:00 Time on the x -axis 0 1 3 4 and 5 here 0 .4 .8 1 .2 1 .6 and 2 now second part graph for acceleration as we have defined acceleration is from equation 2 you can write acceleration is h squared into a square of velocity of 5 upon x square plus h square to the power 3 by 2 here using x is called to velocity of y into t so you may write h square velocity of y is 2 you may write here 2 into t and h is given 6 so 6 square x is 2 2 2 square plus h squared that is 6 square whole to the power 3 by 2 so acceleration you will get 144 divided by 40 square plus 36 whole to the power 3 by 2 now we have to calculate key points substituting the value t 0 .5 and so on and make a table for it here you are using t and acceleration acceleration in meter per second square and time in second 0 .67 at 0 .5 second it becomes 0 .64 at 1 second it becomes 0 .57 at 1 .5 it is 0 .48 2 it becomes 0 .38 2 .5 it becomes 0 .3.

08:42 You will get 0 .24 3 .5 it becomes 0 .3...

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