A particle is moving such that its position coordinates (x,y) are

(2m, 3m) at time t = 0,

(6m, 7m) at time t = 2 s and

(13m, 14m) at time t = 5s.

Average velocity vector \left (\underset{\text{V}}{\rightarrow}_{\text{av}} \right )  from t = 0 to t = 5 s is:

  • Option 1)

    \frac{1}{5}\left (13\hat{i} +14\hat{j} \right )

  • Option 2)

    \frac{7}{3}\left (\hat{i}+\hat{j} \right )

  • Option 3)

    2\left (\hat{i}+\hat{j} \right )

  • Option 4)

    \frac{11}{5}\left (\hat{i}+\hat{j} \right )

 

Answers (1)

As we learnt in

Average Speed -

Amount of total distance covered in total time.

Formula

Average, speed =frac{total , distance, covered}{total , time, taken}

V_{av}= frac{s}{t}

 

- wherein

E.g A body covers a total distance of 50 m with variable speed in 5 sec. Find average speed of body during this time
interval.

V_{av}= frac{s}{t}

Rightarrow frac{50m}{5s}= 10m/s

Average Speed = 10 m/s

 

 

 

 

Average velocity = displacement / time

=\frac{\overrightarrow {r_{2}}-\overrightarrow{r_{1}}}{t_{2}-t_{1}}

=\frac{(13\hat{i}+14\hat{j})-(2\hat{i}+3\hat{j})}{5-0}

= \frac{11}{5}(\hat{i}+\hat{j})

Correct option is 4.


Option 1)

\frac{1}{5}\left (13\hat{i} +14\hat{j} \right )

Incorrect

Option 2)

\frac{7}{3}\left (\hat{i}+\hat{j} \right )

Incorrect

Option 3)

2\left (\hat{i}+\hat{j} \right )

Incorrect

Option 4)

\frac{11}{5}\left (\hat{i}+\hat{j} \right )

Correct

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