A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector from t = 0 to t = 5 s is [2014]

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Q.
A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector $({\vec{v}}_{av})$ from t = 0 to t = 5 s is [2014]

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

2 $\frac{7}{3} (\hat{i} + \hat{j})$

3 $2 (\hat{i} + \hat{j})$

4 $\frac{11}{5} (\hat{i} + \hat{j})$

Ans.
(4)

At time t = 0, the position vector of the particle is ${\vec{r}}_{1} = 2 \hat{i} + 3 \hat{j} .$

At time t = 5 s, the position vector of the particle is ${\vec{r}}_{2} = 13 \hat{i} + 14 \hat{j} .$

Displacement from ${\vec{r}}_{1}$ to ${\vec{r}}_{2}$ is

$Δ \vec{r} = {\vec{r}}_{2} - {\vec{r}}_{1} = (13 \hat{i} + 14 \hat{j}) - (2 \hat{i} + 3 \hat{j}) = 11 \hat{i} + 11 \hat{j}$

$∴ Average velocity, {\vec{v}}_{av} = \frac{Δ \vec{r}}{Δ t} = \frac{11 \hat{i} + 11 \hat{j}}{5 - 0} = \frac{11}{5} (\hat{i} + \hat{j})$

Solution

Q.
A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector $({\vec{v}}_{av})$ from t = 0 to t = 5 s is [2014]

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

2 $\frac{7}{3} (\hat{i} + \hat{j})$

3 $2 (\hat{i} + \hat{j})$

4 $\frac{11}{5} (\hat{i} + \hat{j})$

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Solution

Q. A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector (v→av)from t = 0 to t = 5 s is [2014]

1 15(13i^+14j^)

2 73(i^+j^)

3 2(i^+j^)

4 115(i^+j^)

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Q.
A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m) at time t = 2 s and (13 m, 14 m) at time t = 5 s. Average velocity vector $({\vec{v}}_{av})$ from t = 0 to t = 5 s is [2014]

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

2 $\frac{7}{3} (\hat{i} + \hat{j})$

3 $2 (\hat{i} + \hat{j})$

4 $\frac{11}{5} (\hat{i} + \hat{j})$