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## Displacement of an Object Moving in two dimensions

Displacement of the object can be calculated in a two dimensional motion as shown in the figure.

Concepts

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Displacement of the object can be calculated in a two dimensional motion as shown in the figure.

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S.No | Distance | Displacement |

1. | It is the length of actual path traveled | It is the length of shortest distance between final and initial points |

2. | It is a scalar | It is a vector |

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Velocity is defined as the rate of change of displacement with time.

It is a vector quantity and has units m/s.

The direction of a velocity vector is same as the direction of the motion of body at that instant of time. Magnitude of instantaneous velocity is same as the speed at the instant.

It is a vector quantity and has units m/s.

The direction of a velocity vector is same as the direction of the motion of body at that instant of time. Magnitude of instantaneous velocity is same as the speed at the instant.

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Average acceleration is the change in velocity divided by an elapsed time. For instance, if the velocity of a marble increases from 0 to 60 cm/s in 3 seconds, its average acceleration would be 20 cm/s$_{2}$. This means that the marble's velocity will increase by 20 cm/s every second.

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Displacement time graph for rest is a straight line with zero slope.

Displacement time graph for uniform motion is a straight line with non-zero slope.

Displacement time graph for uniform acceleration is a parabola.

The three scenarios are shown in the attached plot.

Displacement time graph for uniform motion is a straight line with non-zero slope.

Displacement time graph for uniform acceleration is a parabola.

The three scenarios are shown in the attached plot.

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Acceleration vs. time graphs tell us about an object's velocity in the same way that velocity vs. time graphs tell us about an object's displacement. The change in velocity in a given time interval is equal to the area under the graph during that same time interval.

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A swimmer can swim in still water with speed $v$ and the river flowing with velocity $2v $. To cross the river in shortest distance, he should swim making an angle $θ$* *with the upstream. Find ratio of the time taken to swim across in the shortest time to that in swimming across over shortest distance.

For shortest distance , Time taken $=V_{b}sinθW $

For shortest time , Time taken $=V_{b}W $

Ratio of times taken for shortest time to that of shortest path $=V_{b}sinθW V_{b}W =sinθ$

For shortest distance , Time taken $=V_{b}sinθW $

For shortest time , Time taken $=V_{b}W $

Ratio of times taken for shortest time to that of shortest path $=V_{b}sinθW V_{b}W =sinθ$

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In free fall initial velocity of the particle is zero.

Therefore, equations of motion are:

$v=gt.$

$h=2gt_{2} $

and $v_{2}=2gs$

Therefore, equations of motion are:

$v=gt.$

$h=2gt_{2} $

and $v_{2}=2gs$