362311
A body starts moving from rest with constant acceleration covers displacement \(S_{1}\) in first \((p-1)\) seconds and \(S_{2}\) in first \(p\) seconds. The displacement \(S_{1}+S_{2}\) will be made in time
1 \((2 p+1) s\)
2 \(\left(2 p^{2}-2 p+1\right) s\)
3 \(\sqrt{\left(2 p^{2}-2 p+1\right)} s\)
4 \((2 p-1) s\)
Explanation:
Displacement \(S_{1}\) in first \((p-1) s\) and \(p\) seconds are given as : \(S_{1}=\dfrac{1}{2} a(p-1)^{2} \quad(\because\) Initial velocity is 0\()\) \(S_{2}=\dfrac{1}{2} a p^{2}\) Total displacement, \(S_{1}+S_{2}=\dfrac{1}{2} a(p-1)^{2}+\dfrac{1}{2} a p^{2}=\dfrac{1}{2} a t^{2}\) \(\Rightarrow S_{1}+S_{2}=(p-1)^{2}+p^{2}=t^{2}\) \(t=\sqrt{(p-1)^{2}+p^{2}} s ; t=\sqrt{\left(2 p^{2}-2 p+1\right)} s\)
JEE - 2024
PHXI03:MOTION IN A STRAIGHT LINE
362312
A car moving along a straight highway with speed of \(126\,km/h\) is brought to a stop within a distance of 200 \(m\). What is the retardation of the car (assumed uniform) and how long does it take for the car to stop?
1 \(3.06\,m/{s^2}\;{\rm{and}}\;4.1\,s\)
2 \(2.06\,m/{s^2}\;{\rm{and}}\;11.4\,s\)
3 \(3.06\,m/{s^2}\;{\rm{and}}\;11.4\,s\)
4 \(3.06\,m/{s^2}\;{\rm{and}}\;10.4\,s\)
Explanation:
Initial velocity of the car \((u) = 126\,km/h\) \( = 126 \times \frac{5}{{18}}m/s = 35\,m/s\) \(\left( {\because 1km/h = \frac{5}{{18}}m/s} \right)\) Final velocity of the car \((v) = 0\) Distance travelled \((s) = 200\,m\) From equation of motion, \({v^2} = {u^2} + 2as\) or \(a = \frac{{{v^2} - {u^2}}}{{2s}} = \frac{{0 - {{\left( {35} \right)}^2}}}{{2 \times 200}} = - 3.06 \, m/{s^2}\) \(\therefore \) Retardation of motion, \(v = u + at\) \(t = \frac{{v - u}}{a} = \frac{{\left( {0 - 35} \right)}}{{\left( { - 49/16} \right)}} = 11.4\,s\) \(\therefore \) Car will stop after \(11.4\,s\)
NCERT Exemplar
PHXI03:MOTION IN A STRAIGHT LINE
362313
Assertion : Velocity - time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis. Reason : In uniform motion of an object velocity increases as the square of time elapsed.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In uniform motion, an object moves with a constant velocity, meaning that the magnitude of its velocity remains the same at different instants, such as at \(t=0,1\) second, 2 seconds, and so on. Consequently, the velocity-time graph for an object in uniform motion along a straight path is a straight line that runs parallel to the time axis." So correct option is (3).
PHXI03:MOTION IN A STRAIGHT LINE
362314
The velocity of a bullet is reduced from \(200\,m/s\) to 100 \(m/s\), while travelling through a wooden block of thickness \(10\,cm\). Assuming it to be uniform, the magnitude of acceleration will be:
362311
A body starts moving from rest with constant acceleration covers displacement \(S_{1}\) in first \((p-1)\) seconds and \(S_{2}\) in first \(p\) seconds. The displacement \(S_{1}+S_{2}\) will be made in time
1 \((2 p+1) s\)
2 \(\left(2 p^{2}-2 p+1\right) s\)
3 \(\sqrt{\left(2 p^{2}-2 p+1\right)} s\)
4 \((2 p-1) s\)
Explanation:
Displacement \(S_{1}\) in first \((p-1) s\) and \(p\) seconds are given as : \(S_{1}=\dfrac{1}{2} a(p-1)^{2} \quad(\because\) Initial velocity is 0\()\) \(S_{2}=\dfrac{1}{2} a p^{2}\) Total displacement, \(S_{1}+S_{2}=\dfrac{1}{2} a(p-1)^{2}+\dfrac{1}{2} a p^{2}=\dfrac{1}{2} a t^{2}\) \(\Rightarrow S_{1}+S_{2}=(p-1)^{2}+p^{2}=t^{2}\) \(t=\sqrt{(p-1)^{2}+p^{2}} s ; t=\sqrt{\left(2 p^{2}-2 p+1\right)} s\)
JEE - 2024
PHXI03:MOTION IN A STRAIGHT LINE
362312
A car moving along a straight highway with speed of \(126\,km/h\) is brought to a stop within a distance of 200 \(m\). What is the retardation of the car (assumed uniform) and how long does it take for the car to stop?
1 \(3.06\,m/{s^2}\;{\rm{and}}\;4.1\,s\)
2 \(2.06\,m/{s^2}\;{\rm{and}}\;11.4\,s\)
3 \(3.06\,m/{s^2}\;{\rm{and}}\;11.4\,s\)
4 \(3.06\,m/{s^2}\;{\rm{and}}\;10.4\,s\)
Explanation:
Initial velocity of the car \((u) = 126\,km/h\) \( = 126 \times \frac{5}{{18}}m/s = 35\,m/s\) \(\left( {\because 1km/h = \frac{5}{{18}}m/s} \right)\) Final velocity of the car \((v) = 0\) Distance travelled \((s) = 200\,m\) From equation of motion, \({v^2} = {u^2} + 2as\) or \(a = \frac{{{v^2} - {u^2}}}{{2s}} = \frac{{0 - {{\left( {35} \right)}^2}}}{{2 \times 200}} = - 3.06 \, m/{s^2}\) \(\therefore \) Retardation of motion, \(v = u + at\) \(t = \frac{{v - u}}{a} = \frac{{\left( {0 - 35} \right)}}{{\left( { - 49/16} \right)}} = 11.4\,s\) \(\therefore \) Car will stop after \(11.4\,s\)
NCERT Exemplar
PHXI03:MOTION IN A STRAIGHT LINE
362313
Assertion : Velocity - time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis. Reason : In uniform motion of an object velocity increases as the square of time elapsed.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In uniform motion, an object moves with a constant velocity, meaning that the magnitude of its velocity remains the same at different instants, such as at \(t=0,1\) second, 2 seconds, and so on. Consequently, the velocity-time graph for an object in uniform motion along a straight path is a straight line that runs parallel to the time axis." So correct option is (3).
PHXI03:MOTION IN A STRAIGHT LINE
362314
The velocity of a bullet is reduced from \(200\,m/s\) to 100 \(m/s\), while travelling through a wooden block of thickness \(10\,cm\). Assuming it to be uniform, the magnitude of acceleration will be:
362311
A body starts moving from rest with constant acceleration covers displacement \(S_{1}\) in first \((p-1)\) seconds and \(S_{2}\) in first \(p\) seconds. The displacement \(S_{1}+S_{2}\) will be made in time
1 \((2 p+1) s\)
2 \(\left(2 p^{2}-2 p+1\right) s\)
3 \(\sqrt{\left(2 p^{2}-2 p+1\right)} s\)
4 \((2 p-1) s\)
Explanation:
Displacement \(S_{1}\) in first \((p-1) s\) and \(p\) seconds are given as : \(S_{1}=\dfrac{1}{2} a(p-1)^{2} \quad(\because\) Initial velocity is 0\()\) \(S_{2}=\dfrac{1}{2} a p^{2}\) Total displacement, \(S_{1}+S_{2}=\dfrac{1}{2} a(p-1)^{2}+\dfrac{1}{2} a p^{2}=\dfrac{1}{2} a t^{2}\) \(\Rightarrow S_{1}+S_{2}=(p-1)^{2}+p^{2}=t^{2}\) \(t=\sqrt{(p-1)^{2}+p^{2}} s ; t=\sqrt{\left(2 p^{2}-2 p+1\right)} s\)
JEE - 2024
PHXI03:MOTION IN A STRAIGHT LINE
362312
A car moving along a straight highway with speed of \(126\,km/h\) is brought to a stop within a distance of 200 \(m\). What is the retardation of the car (assumed uniform) and how long does it take for the car to stop?
1 \(3.06\,m/{s^2}\;{\rm{and}}\;4.1\,s\)
2 \(2.06\,m/{s^2}\;{\rm{and}}\;11.4\,s\)
3 \(3.06\,m/{s^2}\;{\rm{and}}\;11.4\,s\)
4 \(3.06\,m/{s^2}\;{\rm{and}}\;10.4\,s\)
Explanation:
Initial velocity of the car \((u) = 126\,km/h\) \( = 126 \times \frac{5}{{18}}m/s = 35\,m/s\) \(\left( {\because 1km/h = \frac{5}{{18}}m/s} \right)\) Final velocity of the car \((v) = 0\) Distance travelled \((s) = 200\,m\) From equation of motion, \({v^2} = {u^2} + 2as\) or \(a = \frac{{{v^2} - {u^2}}}{{2s}} = \frac{{0 - {{\left( {35} \right)}^2}}}{{2 \times 200}} = - 3.06 \, m/{s^2}\) \(\therefore \) Retardation of motion, \(v = u + at\) \(t = \frac{{v - u}}{a} = \frac{{\left( {0 - 35} \right)}}{{\left( { - 49/16} \right)}} = 11.4\,s\) \(\therefore \) Car will stop after \(11.4\,s\)
NCERT Exemplar
PHXI03:MOTION IN A STRAIGHT LINE
362313
Assertion : Velocity - time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis. Reason : In uniform motion of an object velocity increases as the square of time elapsed.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In uniform motion, an object moves with a constant velocity, meaning that the magnitude of its velocity remains the same at different instants, such as at \(t=0,1\) second, 2 seconds, and so on. Consequently, the velocity-time graph for an object in uniform motion along a straight path is a straight line that runs parallel to the time axis." So correct option is (3).
PHXI03:MOTION IN A STRAIGHT LINE
362314
The velocity of a bullet is reduced from \(200\,m/s\) to 100 \(m/s\), while travelling through a wooden block of thickness \(10\,cm\). Assuming it to be uniform, the magnitude of acceleration will be:
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI03:MOTION IN A STRAIGHT LINE
362311
A body starts moving from rest with constant acceleration covers displacement \(S_{1}\) in first \((p-1)\) seconds and \(S_{2}\) in first \(p\) seconds. The displacement \(S_{1}+S_{2}\) will be made in time
1 \((2 p+1) s\)
2 \(\left(2 p^{2}-2 p+1\right) s\)
3 \(\sqrt{\left(2 p^{2}-2 p+1\right)} s\)
4 \((2 p-1) s\)
Explanation:
Displacement \(S_{1}\) in first \((p-1) s\) and \(p\) seconds are given as : \(S_{1}=\dfrac{1}{2} a(p-1)^{2} \quad(\because\) Initial velocity is 0\()\) \(S_{2}=\dfrac{1}{2} a p^{2}\) Total displacement, \(S_{1}+S_{2}=\dfrac{1}{2} a(p-1)^{2}+\dfrac{1}{2} a p^{2}=\dfrac{1}{2} a t^{2}\) \(\Rightarrow S_{1}+S_{2}=(p-1)^{2}+p^{2}=t^{2}\) \(t=\sqrt{(p-1)^{2}+p^{2}} s ; t=\sqrt{\left(2 p^{2}-2 p+1\right)} s\)
JEE - 2024
PHXI03:MOTION IN A STRAIGHT LINE
362312
A car moving along a straight highway with speed of \(126\,km/h\) is brought to a stop within a distance of 200 \(m\). What is the retardation of the car (assumed uniform) and how long does it take for the car to stop?
1 \(3.06\,m/{s^2}\;{\rm{and}}\;4.1\,s\)
2 \(2.06\,m/{s^2}\;{\rm{and}}\;11.4\,s\)
3 \(3.06\,m/{s^2}\;{\rm{and}}\;11.4\,s\)
4 \(3.06\,m/{s^2}\;{\rm{and}}\;10.4\,s\)
Explanation:
Initial velocity of the car \((u) = 126\,km/h\) \( = 126 \times \frac{5}{{18}}m/s = 35\,m/s\) \(\left( {\because 1km/h = \frac{5}{{18}}m/s} \right)\) Final velocity of the car \((v) = 0\) Distance travelled \((s) = 200\,m\) From equation of motion, \({v^2} = {u^2} + 2as\) or \(a = \frac{{{v^2} - {u^2}}}{{2s}} = \frac{{0 - {{\left( {35} \right)}^2}}}{{2 \times 200}} = - 3.06 \, m/{s^2}\) \(\therefore \) Retardation of motion, \(v = u + at\) \(t = \frac{{v - u}}{a} = \frac{{\left( {0 - 35} \right)}}{{\left( { - 49/16} \right)}} = 11.4\,s\) \(\therefore \) Car will stop after \(11.4\,s\)
NCERT Exemplar
PHXI03:MOTION IN A STRAIGHT LINE
362313
Assertion : Velocity - time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis. Reason : In uniform motion of an object velocity increases as the square of time elapsed.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In uniform motion, an object moves with a constant velocity, meaning that the magnitude of its velocity remains the same at different instants, such as at \(t=0,1\) second, 2 seconds, and so on. Consequently, the velocity-time graph for an object in uniform motion along a straight path is a straight line that runs parallel to the time axis." So correct option is (3).
PHXI03:MOTION IN A STRAIGHT LINE
362314
The velocity of a bullet is reduced from \(200\,m/s\) to 100 \(m/s\), while travelling through a wooden block of thickness \(10\,cm\). Assuming it to be uniform, the magnitude of acceleration will be:
