SATHEE: Motion in a Straight Line

Motion in a Straight Line - Result Question 15

15. A particle has initial velocity $(3 \hat{i} + 4 \hat{j})$ and has acceleration $(0.4 \hat{i} + 0.3 \hat{j})$ . It’s speed after 10 $s$ is:

[2010]

(a) 7 units

(b) $7 \sqrt{2}$ units

(d) 10 units

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Answer:

Correct Answer: 15. (b)

Solution:

(b) Given, $\vec{u} = 3 \hat{i} + 4 \hat{j}$ and $\vec{a} = 0.4 \hat{i} + 0.3 \hat{j}$

$\Rightarrow u_{x} = 3$ units, $u_{y} = 4$ units

$\Rightarrow a_{x} = 0.4$ units, $a_{y} = 0.3$ units

Along $x$ -axis,

$∴ v_{x} = u_{x} + a_{x} \times 10 = 3 + 4 = 7$ units

Along $y$ -axis,

and $v_{y} = 4 + 0.3 \times 10 = 4 + 3 = 7$ units

Net final velocity $∴ v = \sqrt{v_{x}^{2} + v_{y}^{2}} = 7 \sqrt{2}$ units

${\vec{v}}_{i} = 3 \hat{i} + 4 \hat{j}$ and $\vec{a} = 0.4 \hat{i} + 0.3 \hat{j}$

time, $t = 10 s e c$ .

Final velocity ${\vec{v}}_{f}$ after time $t = 10 s e c, {\vec{v}}_{f} = {\vec{v}}_{i} + \vec{a} t$

${\vec{v}}_{f} = (3 \hat{i} + 4 \hat{j}) + (0.4 \hat{i} + 0.3 \hat{j}) (10) = 7 \hat{i} + 7 \hat{j}$

The particle speeds up i.e., the speed of the particle increases when the angle between $\vec{a}$ and $\vec{v}$ lies between $0^{\circ} + 90^{\circ}$ . The particle speeds down i.e., the speed of the particle decreases when the angle between $\vec{a}$ and $\vec{v}$ lies between $+ 90^{\circ}$ and $180^{\circ}$ .

Motion in a Straight Line - Result Question 15

15. A particle has initial velocity $(3 \hat{i} + 4 \hat{j})$ and has acceleration $(0.4 \hat{i} + 0.3 \hat{j})$ . It’s speed after 10 $s$ is:

Answer:

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Motion in a Straight Line - Result Question 15

15. A particle has initial velocity (3i^+4j^) and has acceleration (0.4i^+0.3j^). It’s speed after 10 s is:

Answer:

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15. A particle has initial velocity $(3 \hat{i} + 4 \hat{j})$ and has acceleration $(0.4 \hat{i} + 0.3 \hat{j})$ . It’s speed after 10 $s$ is: