ACCELERATION
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MOTION IN A STRIGHT LINE

269797 Two cars start in a race with velocities\(u_{1}\) and \(u_{2}\) and travel in a straight line with accelerations ' \(\alpha\) ' and \(\beta\). If both reach the finish line at the same time, the range of the race is

1 \(\frac{2\left(u_{1}-u_{2}\right)}{(\beta-\alpha)^{2}}\left(u_{1} \beta-u_{2} \alpha\right)\)
2 \(\frac{2\left(u_{1}-u_{2}\right)}{\beta+\alpha}\left(u_{1} \alpha-u_{2} \beta\right)\)
3 \(\frac{2\left(u_{1}-u_{2}\right)^{2}}{(\beta-\alpha)^{2}}\)
4 \(\frac{2 \mathrm{u}_{1} \mathrm{u}_{2}}{\beta \alpha}\)
MOTION IN A STRIGHT LINE

269798 A point moves with uniform acceleration \(\mathrm{v}_{1}, \mathrm{v}_{2}\) and \(\mathrm{v}_{3}\) denote the average velocities in three successive intervals of time \(t, t, t\) and \(t_{3}\). Correct relation among the following is

1 \(\left(\mathrm{v}_{1}-\mathrm{v}_{2}\right):\left(\mathrm{v}_{2}-\mathrm{v}_{3}\right)=\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right):\left(\mathrm{t}_{-}-\mathrm{t}_{3}\right)\)
2 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}+t_{3}\right)\)
3 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}+t_{3}\right)\)
4 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}-t_{3}\right)\)
MOTION IN A STRIGHT LINE

269799 A trainstartsfrom rest and moves with uniform acceleration \(\alpha\) for sometime and acquires a velocity ' \(v\) '. It then moves with constant velocity for some time and then decelerates
at rate \(\beta\) and finally comes to rest at thenext station. If ' \(L\) ' isdistance between two stations then total time of travel is

1 \(\frac{L}{v}+\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\)
2 \(\frac{L}{v}-\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\)
3 \(\frac{\mathrm{L}}{\mathrm{v}}-\frac{\mathrm{v}}{2}\left(\frac{1}{\alpha}-\frac{1}{\beta}\right)\)
4 \(\frac{L}{v}+\frac{v}{2}\left(\frac{1}{\alpha}-\frac{1}{\beta}\right)\)
MOTION IN A STRIGHT LINE

269800 A car, starting from rest, accelerates at theratef through a distances, then continues at constant speed for timet and then decelerate at the rate ( \(f / 2\) ) to come to rest. If the total distance travelled is \(15 S\), then

1 \(S=\mathrm{ft}\)
2 \(S=\frac{1}{6} \mathrm{ft}^{2}\)
3 \(\mathrm{S}=\frac{1}{72} \mathrm{ft}^{2}\)
4 \(S=\frac{1}{4} \mathrm{ft}^{2}\)
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MOTION IN A STRIGHT LINE

269797 Two cars start in a race with velocities\(u_{1}\) and \(u_{2}\) and travel in a straight line with accelerations ' \(\alpha\) ' and \(\beta\). If both reach the finish line at the same time, the range of the race is

1 \(\frac{2\left(u_{1}-u_{2}\right)}{(\beta-\alpha)^{2}}\left(u_{1} \beta-u_{2} \alpha\right)\)
2 \(\frac{2\left(u_{1}-u_{2}\right)}{\beta+\alpha}\left(u_{1} \alpha-u_{2} \beta\right)\)
3 \(\frac{2\left(u_{1}-u_{2}\right)^{2}}{(\beta-\alpha)^{2}}\)
4 \(\frac{2 \mathrm{u}_{1} \mathrm{u}_{2}}{\beta \alpha}\)
MOTION IN A STRIGHT LINE

269798 A point moves with uniform acceleration \(\mathrm{v}_{1}, \mathrm{v}_{2}\) and \(\mathrm{v}_{3}\) denote the average velocities in three successive intervals of time \(t, t, t\) and \(t_{3}\). Correct relation among the following is

1 \(\left(\mathrm{v}_{1}-\mathrm{v}_{2}\right):\left(\mathrm{v}_{2}-\mathrm{v}_{3}\right)=\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right):\left(\mathrm{t}_{-}-\mathrm{t}_{3}\right)\)
2 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}+t_{3}\right)\)
3 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}+t_{3}\right)\)
4 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}-t_{3}\right)\)
MOTION IN A STRIGHT LINE

269799 A trainstartsfrom rest and moves with uniform acceleration \(\alpha\) for sometime and acquires a velocity ' \(v\) '. It then moves with constant velocity for some time and then decelerates
at rate \(\beta\) and finally comes to rest at thenext station. If ' \(L\) ' isdistance between two stations then total time of travel is

1 \(\frac{L}{v}+\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\)
2 \(\frac{L}{v}-\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\)
3 \(\frac{\mathrm{L}}{\mathrm{v}}-\frac{\mathrm{v}}{2}\left(\frac{1}{\alpha}-\frac{1}{\beta}\right)\)
4 \(\frac{L}{v}+\frac{v}{2}\left(\frac{1}{\alpha}-\frac{1}{\beta}\right)\)
MOTION IN A STRIGHT LINE

269800 A car, starting from rest, accelerates at theratef through a distances, then continues at constant speed for timet and then decelerate at the rate ( \(f / 2\) ) to come to rest. If the total distance travelled is \(15 S\), then

1 \(S=\mathrm{ft}\)
2 \(S=\frac{1}{6} \mathrm{ft}^{2}\)
3 \(\mathrm{S}=\frac{1}{72} \mathrm{ft}^{2}\)
4 \(S=\frac{1}{4} \mathrm{ft}^{2}\)
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MOTION IN A STRIGHT LINE

269797 Two cars start in a race with velocities\(u_{1}\) and \(u_{2}\) and travel in a straight line with accelerations ' \(\alpha\) ' and \(\beta\). If both reach the finish line at the same time, the range of the race is

1 \(\frac{2\left(u_{1}-u_{2}\right)}{(\beta-\alpha)^{2}}\left(u_{1} \beta-u_{2} \alpha\right)\)
2 \(\frac{2\left(u_{1}-u_{2}\right)}{\beta+\alpha}\left(u_{1} \alpha-u_{2} \beta\right)\)
3 \(\frac{2\left(u_{1}-u_{2}\right)^{2}}{(\beta-\alpha)^{2}}\)
4 \(\frac{2 \mathrm{u}_{1} \mathrm{u}_{2}}{\beta \alpha}\)
MOTION IN A STRIGHT LINE

269798 A point moves with uniform acceleration \(\mathrm{v}_{1}, \mathrm{v}_{2}\) and \(\mathrm{v}_{3}\) denote the average velocities in three successive intervals of time \(t, t, t\) and \(t_{3}\). Correct relation among the following is

1 \(\left(\mathrm{v}_{1}-\mathrm{v}_{2}\right):\left(\mathrm{v}_{2}-\mathrm{v}_{3}\right)=\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right):\left(\mathrm{t}_{-}-\mathrm{t}_{3}\right)\)
2 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}+t_{3}\right)\)
3 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}+t_{3}\right)\)
4 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}-t_{3}\right)\)
MOTION IN A STRIGHT LINE

269799 A trainstartsfrom rest and moves with uniform acceleration \(\alpha\) for sometime and acquires a velocity ' \(v\) '. It then moves with constant velocity for some time and then decelerates
at rate \(\beta\) and finally comes to rest at thenext station. If ' \(L\) ' isdistance between two stations then total time of travel is

1 \(\frac{L}{v}+\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\)
2 \(\frac{L}{v}-\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\)
3 \(\frac{\mathrm{L}}{\mathrm{v}}-\frac{\mathrm{v}}{2}\left(\frac{1}{\alpha}-\frac{1}{\beta}\right)\)
4 \(\frac{L}{v}+\frac{v}{2}\left(\frac{1}{\alpha}-\frac{1}{\beta}\right)\)
MOTION IN A STRIGHT LINE

269800 A car, starting from rest, accelerates at theratef through a distances, then continues at constant speed for timet and then decelerate at the rate ( \(f / 2\) ) to come to rest. If the total distance travelled is \(15 S\), then

1 \(S=\mathrm{ft}\)
2 \(S=\frac{1}{6} \mathrm{ft}^{2}\)
3 \(\mathrm{S}=\frac{1}{72} \mathrm{ft}^{2}\)
4 \(S=\frac{1}{4} \mathrm{ft}^{2}\)
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MOTION IN A STRIGHT LINE

269797 Two cars start in a race with velocities\(u_{1}\) and \(u_{2}\) and travel in a straight line with accelerations ' \(\alpha\) ' and \(\beta\). If both reach the finish line at the same time, the range of the race is

1 \(\frac{2\left(u_{1}-u_{2}\right)}{(\beta-\alpha)^{2}}\left(u_{1} \beta-u_{2} \alpha\right)\)
2 \(\frac{2\left(u_{1}-u_{2}\right)}{\beta+\alpha}\left(u_{1} \alpha-u_{2} \beta\right)\)
3 \(\frac{2\left(u_{1}-u_{2}\right)^{2}}{(\beta-\alpha)^{2}}\)
4 \(\frac{2 \mathrm{u}_{1} \mathrm{u}_{2}}{\beta \alpha}\)
MOTION IN A STRIGHT LINE

269798 A point moves with uniform acceleration \(\mathrm{v}_{1}, \mathrm{v}_{2}\) and \(\mathrm{v}_{3}\) denote the average velocities in three successive intervals of time \(t, t, t\) and \(t_{3}\). Correct relation among the following is

1 \(\left(\mathrm{v}_{1}-\mathrm{v}_{2}\right):\left(\mathrm{v}_{2}-\mathrm{v}_{3}\right)=\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right):\left(\mathrm{t}_{-}-\mathrm{t}_{3}\right)\)
2 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}+t_{3}\right)\)
3 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}-t_{2}\right):\left(t_{2}+t_{3}\right)\)
4 \(\left(v_{1}-v_{2}\right):\left(v_{2}-v_{3}\right)=\left(t_{1}+t_{2}\right):\left(t_{2}-t_{3}\right)\)
MOTION IN A STRIGHT LINE

269799 A trainstartsfrom rest and moves with uniform acceleration \(\alpha\) for sometime and acquires a velocity ' \(v\) '. It then moves with constant velocity for some time and then decelerates
at rate \(\beta\) and finally comes to rest at thenext station. If ' \(L\) ' isdistance between two stations then total time of travel is

1 \(\frac{L}{v}+\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\)
2 \(\frac{L}{v}-\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\)
3 \(\frac{\mathrm{L}}{\mathrm{v}}-\frac{\mathrm{v}}{2}\left(\frac{1}{\alpha}-\frac{1}{\beta}\right)\)
4 \(\frac{L}{v}+\frac{v}{2}\left(\frac{1}{\alpha}-\frac{1}{\beta}\right)\)
MOTION IN A STRIGHT LINE

269800 A car, starting from rest, accelerates at theratef through a distances, then continues at constant speed for timet and then decelerate at the rate ( \(f / 2\) ) to come to rest. If the total distance travelled is \(15 S\), then

1 \(S=\mathrm{ft}\)
2 \(S=\frac{1}{6} \mathrm{ft}^{2}\)
3 \(\mathrm{S}=\frac{1}{72} \mathrm{ft}^{2}\)
4 \(S=\frac{1}{4} \mathrm{ft}^{2}\)
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