Turito Academy

Test Prep

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Slope of displacement time-graph is velocity<br /><img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator v subscript 1 end subscript over denominator v subscript 2 end subscript end fraction equals fraction numerator tan invisible function application theta subscript 1 end subscript over denominator tan invisible function application theta subscript 2 end subscript end fraction equals fraction numerator tan invisible function application 30 degree over denominator tan invisible function application 45 degree end fraction equals fraction numerator 1 over denominator square root of 3 end fraction" width="221" height="46" style="vertical-align:-19px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msub»«mrow»«mi»v«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/mrow»«mrow»«msub»«mrow»«mi»v«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mrow»«mrow»«mi»tan«/mi»«/mrow»«mo»⁡«/mo»«mrow»«msub»«mrow»«mi»θ«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/mrow»«/mrow»«/mrow»«mrow»«mrow»«mrow»«mi»tan«/mi»«/mrow»«mo»⁡«/mo»«mrow»«msub»«mrow»«mi»θ«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/mrow»«/mrow»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mrow»«mrow»«mi»tan«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»30«/mn»«mo»°«/mo»«/mrow»«/mrow»«/mrow»«mrow»«mrow»«mrow»«mi»tan«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»45«/mn»«mo»°«/mo»«/mrow»«/mrow»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfrac»«/math»'/><br /><img src="data:image/png;base64,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" class="Wirisformula" alt="v subscript 1 end subscript blank colon v subscript 2 end subscript equals 1 blank colon blank square root of 3" width="114" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»v«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«mi» «/mi»«mo»:«/mo»«msub»«mrow»«mi»v«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«mo»=«/mo»«mn»1«/mn»«mi» «/mi»«mo»:«/mo»«mi» «/mi»«msqrt»«mn»3«/mn»«/msqrt»«/math»'/>

The displacement-time graphs of two moving particles make angles of <img src="data:image/png;base64,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" class="Wirisformula" alt="30 degree blank a n d blank 45 degree" width="90" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»30«/mn»«mo»°«/mo»«mi» «/mi»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mi» «/mi»«mn»45«/mn»«mo»°«/mo»«/math»'/> with the <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAKCAYAAACuaZ5oAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHpJREFUeNpjYECAZCDuYMAEzVA5qoBzQCyOxE8E4ikMVAQeQNwHZbsA8V4GGoDdQGwPxBeAWBiHmv9EYJygAIh/AbEeLVxvDcRroMEUSW3DlYB4ExBzATEPEJ/BE0QkA1Eg3oZmoA8QL6aG4WxAvA6IpbHILYemrMELAKDvGRHa7zegAAAAU3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48bW8+LTwvbW8+PC9tYXRoPo8hS6cAAAAASUVORK5CYII=" class="Wirisformula" alt="x minus" width="24" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mo»-«/mo»«/math»'/>axis. The ratio of their velocities is<br /><img src="data:image/png;base64,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" alt="" />

Solution for the question - the displacement-time graphs of two moving particles make angles of 30 and45 with the x- axis. the ratio of their velocities is sqrt3:2