Kinematic Equations
PHXI03:MOTION IN A STRAIGHT LINE

362306 A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\,m{s^{ - 1}}\) to \(20\,m{s^{ - 1}}\) while passing through a distance \(135\,m\) in \(t\) sec. The value of \(t\) is

1 \(10\)
2 \(9\)
3 \(12\)
4 \(1.8\)
PHXI03:MOTION IN A STRAIGHT LINE

362307 Statement A :
Doubling the initial velocity, the stopping distance of moving object increases by a factor of 4 (for the same deceleration).
Statement B :
Stopping distance is proportional to the initial velocity.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362308 Two cars \(A\) and \(B\) are travelling in the same direction with velocities \({v_{\rm{A}}}\,{\rm{and}}\,{v_B}\left( {{v_{\rm{A}}} > {v_{\rm{B}}}} \right)\). The initial seperation between the cars is \(d\). When the car \(A\) applies brakes producing a uniform retardation \(a\). There will be no collision when

1 \(d < \frac{(v_A - v_B)^2}{2a}\)
2 \(d < \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
3 \(d > \frac{(v_A - v_B)^2}{2a}\)
4 \(d > \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
PHXI03:MOTION IN A STRAIGHT LINE

362309 A car acceleration from rest at a constant rate \(\alpha \) for some time, after which it decelerates at a constant rate \(\beta \) and comes to rest. If the total time elapsed is \(t\), then the maximum velocity acquired by the car is

1 \(\frac{{\left( {\alpha + \beta } \right)t}}{{\alpha \beta }}\)
2 \(\frac{{\alpha \beta t}}{{\alpha + \beta }}\)
3 \(\left( {\frac{{{\alpha ^2} + {\beta ^2}}}{{\alpha \beta }}} \right)t\)
4 \(\left( {\frac{{{\alpha ^2} - {\beta ^2}}}{{\alpha \beta }}} \right)t\)
PHXI03:MOTION IN A STRAIGHT LINE

362310 A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during \(8^{\text {th }}\) second to that covered in 8 seconds is:

1 \(\dfrac{15}{60}\)
2 \(\dfrac{15}{64}\)
3 \(\dfrac{12}{15}\)
4 1
PHXI03:MOTION IN A STRAIGHT LINE

362306 A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\,m{s^{ - 1}}\) to \(20\,m{s^{ - 1}}\) while passing through a distance \(135\,m\) in \(t\) sec. The value of \(t\) is

1 \(10\)
2 \(9\)
3 \(12\)
4 \(1.8\)
PHXI03:MOTION IN A STRAIGHT LINE

362307 Statement A :
Doubling the initial velocity, the stopping distance of moving object increases by a factor of 4 (for the same deceleration).
Statement B :
Stopping distance is proportional to the initial velocity.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362308 Two cars \(A\) and \(B\) are travelling in the same direction with velocities \({v_{\rm{A}}}\,{\rm{and}}\,{v_B}\left( {{v_{\rm{A}}} > {v_{\rm{B}}}} \right)\). The initial seperation between the cars is \(d\). When the car \(A\) applies brakes producing a uniform retardation \(a\). There will be no collision when

1 \(d < \frac{(v_A - v_B)^2}{2a}\)
2 \(d < \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
3 \(d > \frac{(v_A - v_B)^2}{2a}\)
4 \(d > \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
PHXI03:MOTION IN A STRAIGHT LINE

362309 A car acceleration from rest at a constant rate \(\alpha \) for some time, after which it decelerates at a constant rate \(\beta \) and comes to rest. If the total time elapsed is \(t\), then the maximum velocity acquired by the car is

1 \(\frac{{\left( {\alpha + \beta } \right)t}}{{\alpha \beta }}\)
2 \(\frac{{\alpha \beta t}}{{\alpha + \beta }}\)
3 \(\left( {\frac{{{\alpha ^2} + {\beta ^2}}}{{\alpha \beta }}} \right)t\)
4 \(\left( {\frac{{{\alpha ^2} - {\beta ^2}}}{{\alpha \beta }}} \right)t\)
PHXI03:MOTION IN A STRAIGHT LINE

362310 A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during \(8^{\text {th }}\) second to that covered in 8 seconds is:

1 \(\dfrac{15}{60}\)
2 \(\dfrac{15}{64}\)
3 \(\dfrac{12}{15}\)
4 1
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PHXI03:MOTION IN A STRAIGHT LINE

362306 A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\,m{s^{ - 1}}\) to \(20\,m{s^{ - 1}}\) while passing through a distance \(135\,m\) in \(t\) sec. The value of \(t\) is

1 \(10\)
2 \(9\)
3 \(12\)
4 \(1.8\)
PHXI03:MOTION IN A STRAIGHT LINE

362307 Statement A :
Doubling the initial velocity, the stopping distance of moving object increases by a factor of 4 (for the same deceleration).
Statement B :
Stopping distance is proportional to the initial velocity.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362308 Two cars \(A\) and \(B\) are travelling in the same direction with velocities \({v_{\rm{A}}}\,{\rm{and}}\,{v_B}\left( {{v_{\rm{A}}} > {v_{\rm{B}}}} \right)\). The initial seperation between the cars is \(d\). When the car \(A\) applies brakes producing a uniform retardation \(a\). There will be no collision when

1 \(d < \frac{(v_A - v_B)^2}{2a}\)
2 \(d < \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
3 \(d > \frac{(v_A - v_B)^2}{2a}\)
4 \(d > \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
PHXI03:MOTION IN A STRAIGHT LINE

362309 A car acceleration from rest at a constant rate \(\alpha \) for some time, after which it decelerates at a constant rate \(\beta \) and comes to rest. If the total time elapsed is \(t\), then the maximum velocity acquired by the car is

1 \(\frac{{\left( {\alpha + \beta } \right)t}}{{\alpha \beta }}\)
2 \(\frac{{\alpha \beta t}}{{\alpha + \beta }}\)
3 \(\left( {\frac{{{\alpha ^2} + {\beta ^2}}}{{\alpha \beta }}} \right)t\)
4 \(\left( {\frac{{{\alpha ^2} - {\beta ^2}}}{{\alpha \beta }}} \right)t\)
PHXI03:MOTION IN A STRAIGHT LINE

362310 A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during \(8^{\text {th }}\) second to that covered in 8 seconds is:

1 \(\dfrac{15}{60}\)
2 \(\dfrac{15}{64}\)
3 \(\dfrac{12}{15}\)
4 1
PHXI03:MOTION IN A STRAIGHT LINE

362306 A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\,m{s^{ - 1}}\) to \(20\,m{s^{ - 1}}\) while passing through a distance \(135\,m\) in \(t\) sec. The value of \(t\) is

1 \(10\)
2 \(9\)
3 \(12\)
4 \(1.8\)
PHXI03:MOTION IN A STRAIGHT LINE

362307 Statement A :
Doubling the initial velocity, the stopping distance of moving object increases by a factor of 4 (for the same deceleration).
Statement B :
Stopping distance is proportional to the initial velocity.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362308 Two cars \(A\) and \(B\) are travelling in the same direction with velocities \({v_{\rm{A}}}\,{\rm{and}}\,{v_B}\left( {{v_{\rm{A}}} > {v_{\rm{B}}}} \right)\). The initial seperation between the cars is \(d\). When the car \(A\) applies brakes producing a uniform retardation \(a\). There will be no collision when

1 \(d < \frac{(v_A - v_B)^2}{2a}\)
2 \(d < \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
3 \(d > \frac{(v_A - v_B)^2}{2a}\)
4 \(d > \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
PHXI03:MOTION IN A STRAIGHT LINE

362309 A car acceleration from rest at a constant rate \(\alpha \) for some time, after which it decelerates at a constant rate \(\beta \) and comes to rest. If the total time elapsed is \(t\), then the maximum velocity acquired by the car is

1 \(\frac{{\left( {\alpha + \beta } \right)t}}{{\alpha \beta }}\)
2 \(\frac{{\alpha \beta t}}{{\alpha + \beta }}\)
3 \(\left( {\frac{{{\alpha ^2} + {\beta ^2}}}{{\alpha \beta }}} \right)t\)
4 \(\left( {\frac{{{\alpha ^2} - {\beta ^2}}}{{\alpha \beta }}} \right)t\)
PHXI03:MOTION IN A STRAIGHT LINE

362310 A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during \(8^{\text {th }}\) second to that covered in 8 seconds is:

1 \(\dfrac{15}{60}\)
2 \(\dfrac{15}{64}\)
3 \(\dfrac{12}{15}\)
4 1
PHXI03:MOTION IN A STRAIGHT LINE

362306 A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\,m{s^{ - 1}}\) to \(20\,m{s^{ - 1}}\) while passing through a distance \(135\,m\) in \(t\) sec. The value of \(t\) is

1 \(10\)
2 \(9\)
3 \(12\)
4 \(1.8\)
PHXI03:MOTION IN A STRAIGHT LINE

362307 Statement A :
Doubling the initial velocity, the stopping distance of moving object increases by a factor of 4 (for the same deceleration).
Statement B :
Stopping distance is proportional to the initial velocity.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362308 Two cars \(A\) and \(B\) are travelling in the same direction with velocities \({v_{\rm{A}}}\,{\rm{and}}\,{v_B}\left( {{v_{\rm{A}}} > {v_{\rm{B}}}} \right)\). The initial seperation between the cars is \(d\). When the car \(A\) applies brakes producing a uniform retardation \(a\). There will be no collision when

1 \(d < \frac{(v_A - v_B)^2}{2a}\)
2 \(d < \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
3 \(d > \frac{(v_A - v_B)^2}{2a}\)
4 \(d > \frac{{v^{2}_A} - {{v^{2}}_B}}{2a}\)
PHXI03:MOTION IN A STRAIGHT LINE

362309 A car acceleration from rest at a constant rate \(\alpha \) for some time, after which it decelerates at a constant rate \(\beta \) and comes to rest. If the total time elapsed is \(t\), then the maximum velocity acquired by the car is

1 \(\frac{{\left( {\alpha + \beta } \right)t}}{{\alpha \beta }}\)
2 \(\frac{{\alpha \beta t}}{{\alpha + \beta }}\)
3 \(\left( {\frac{{{\alpha ^2} + {\beta ^2}}}{{\alpha \beta }}} \right)t\)
4 \(\left( {\frac{{{\alpha ^2} - {\beta ^2}}}{{\alpha \beta }}} \right)t\)
PHXI03:MOTION IN A STRAIGHT LINE

362310 A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during \(8^{\text {th }}\) second to that covered in 8 seconds is:

1 \(\dfrac{15}{60}\)
2 \(\dfrac{15}{64}\)
3 \(\dfrac{12}{15}\)
4 1