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Displacement

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<h2><span style="font-family:Times New Roman,Times,serif"><span style="font-size:14pt"><span style="color:#0070c0"><strong>Displacement</strong></span></span></span></h2> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">In Physics, it is important to understand about displacement. We will also learn the displacement formula as well as displacement reaction and work on some examples to get a comprehensive idea about it.</span></span></span></p> <h2><span style="font-family:Times New Roman,Times,serif"><span style="font-size:14pt"><span style="color:#0070c0"><strong>What is displacement?</strong></span></span></span></h2> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">The calculation of the shortest distance between starting point and final point which prefers straight-line path over curved paths is known as displacement. </span></span></span></p> <h2><span style="font-family:Times New Roman,Times,serif"><span style="font-size:14pt"><span style="color:#0070c0"><strong>What is displacement formula?</strong></span></span></span></h2> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">If we assume that there is a movement of a body in two different directions x and y then Resultant Displacement will be&nbsp; &nbsp; &nbsp; &nbsp;</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">S = / x<sup>2</sup> + y<sup>2</sup></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">For the given original paths, we provide the shortcut paths</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">S = vt</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">S = 1/2 (u + v) t</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">S = ut + 1/2&nbsp;at<sup>2</sup> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">Here,</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">u = Initial velocity</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">v = final velocity</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">a = acceleration</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">t = time taken.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">Let us have a look a few examples to get some good idea about it.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Question 1:</strong> <strong>Rohan travels 250 miles to North but then back-tracks to South for 105 miles to pick up a friend. Can you find the total displacement of Rohan?</strong></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Solution:&nbsp; </strong>The starting position of Rohan is&nbsp; Xi= 0.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">His final position Xf is the distance travelled N minus the distance South.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">So, we need to calculate displacement, i.e. D.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">We get,</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">D = &Delta;X = (Xf &ndash; Xi)</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">D = (250 mi N &ndash; 105 mi S) &ndash; 0</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">D = 145 mi N</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">So, <strong>the total displacement of Rohan is </strong>145 mi N.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Question 2: Shabib covers 3 rounds on a circular track of radius 50 m. Can you find the total distance and displacement traveled by him?</strong></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Solution: </strong>The total distance Shabib covered =3x circumference of the track</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">We know,</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">Distance = 3 x 2n x 50m</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 300n m (or)</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 300 x 3.14 = 942m</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">Since the athlete reached the same point A, the displacement is zero, after three rounds from where he started.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Related Videos:</strong></span></span></span></p> <ul> <li><span style="font-family:Times New Roman,Times,serif"><span style="font-size:16px"><span style="color:black"><a href="https://doubtnut.com/question-answer-physics/translatory-motion-9773955" style="color:blue; text-decoration:underline">Translatory Motion</a></span></span></span></li> <li><span style="font-family:Times New Roman,Times,serif"><span style="font-size:16px"><span style="color:black"><a href="https://doubtnut.com/question-answer-physics/path-or-trajectory-9773956" style="color:blue; text-decoration:underline">Path or Trajectory</a></span></span></span></li> <li><span style="font-family:Times New Roman,Times,serif"><span style="font-size:16px"><span style="color:black"><a href="https://doubtnut.com/question-answer-physics/trajectory-equation-9773957" style="color:blue; text-decoration:underline">Trajectory Equation</a></span></span></span></li> <li><span style="font-family:Times New Roman,Times,serif"><span style="font-size:16px"><span style="color:black"><a href="https://doubtnut.com/question-answer-physics/distance-formulae-9773959" style="color:blue; text-decoration:underline">Distance Formulae</a></span></span></span></li> <li><span style="font-family:Times New Roman,Times,serif"><span style="font-size:16px"><span style="color:black"><a href="https://doubtnut.com/question-answer-physics/average-velocity-and-average-speed-9773960" style="color:blue; text-decoration:underline">Average Velocity And Average Speed</a></span></span></span></li> </ul> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Question 3: An object begins to move along the grid through points A, B, C, D, E, and F as shown below. The side of square tiles measures 0.5 km.</strong></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>a) Can you find the distance covered by the moving object?</strong></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>b) Calculate the magnitude of the displacement of the object.</strong></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><img alt="displacement of the object" src="https://d10lpgp6xz60nq.cloudfront.net/engagement_framework/5B381E9F-8B75-4757-5EB8-2C2C0A3A5C19.webp" style="height:170px; width:280px" /></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Solution: </strong></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">a) We will calculate the distance covered by the moving object as below:</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">Here, AB + BC + CD + DE + EF</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">So, 3 + 1 + 1.5 + 0.5 + 0.5 = 6.5 km</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">Therefore the distance which is covered by the moving object is 6.5 km.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">b)&nbsp; We will now make the <strong>calculation of the magnitude of the displacement of the object.</strong></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">A and F are the initial point and the final point respectively. Therefore the magnitude of the displacement is equal to the distance AF. So, we will now calculate with the application of Pythagora&rsquo;s theorem to the triangle AHF as shown in the figure below</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><img alt="Pythagora’s theorem to the triangle" src="https://d10lpgp6xz60nq.cloudfront.net/engagement_framework/6C51A6AD-BABA-D0FC-F1AD-3C8ECD350495.webp" style="height:170px; width:280px" /></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">By applying the Pythagorean formula, we get</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">AF<sup>2 </sup>= AH<sup>2 </sup>+ HF<sup>2</sup></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">Now, we need to substitute the formula where we get</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">AF<sup>2</sup> = (0.5 &times; 4)<sup>2 </sup>+ (0.5 &times; 3)<sup>2</sup> =6.25</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">So, AF=6.25km&minus;&minus;&minus;&minus;&minus;&minus;&radic;=2.5km</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">Therefore, the magnitude of displacement is 2.5 km.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Question 4: There are four objects that move according to the paths shown in the diagram below. Can you find the units of the horizontal scale which are given in meters?</strong></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><img alt="horizontal scale " src="https://d10lpgp6xz60nq.cloudfront.net/engagement_framework/A032887F-4FFA-2DF1-8F1B-2F0B76BEDC47.webp" style="height:170px; width:280px" /></span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Solution: </strong>Here, we can see that the total distance object A travels = 7m</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">The total distance object B travels = 5m</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">The total distance object C travels = 8m + 2m +2m = 12m</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px">The total distance object D travels = 6m + 2m = 8m.</span></span></span></p> <p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong>Important Chapters:</strong></span></span></span></p> <ul> <li><span style="font-family:Times New Roman,Times,serif"><span style="font-size:16px"><span style="color:black"><a href="https://doubtnut.com/physics-ncert-solutions" style="color:blue; text-decoration:underline">NCERT Solution for Physics</a></span></span></span></li> <li><span style="font-family:Times New Roman,Times,serif"><span style="font-size:16px"><span style="color:black"><a href="https://doubtnut.com/physics-ncert-solutions/class-11-physics-chapter-3-motion-in-a-straight-line-exercise-1" style="color:blue; text-decoration:underline">NCERT Solution for Class 11 Physics Chapter Motion In A Straight Line</a></span></span></span></li> </ul>

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