The position of a moving particle at time \(t\) is \(\vec{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.\) Its displacement during the time interval \(t=1\) s to \(t=3\) s will be:
1. | \(\hat{j}-\hat{k}\) | 2. | \(3\hat{i}-4\hat{j}-\hat{k}\) |
3. | \(9\hat{i}+36\hat{j}-27\hat{k}\) | 4. | \(32\hat{j}-26\hat{k}\) |
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A cat is situated at point \(A\) (\(0,3,4\)) and a rat is situated at point \(B\) (\(5,3,-8\)). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. 5 unit
2. 12 unit
3. 13 unit
4. 17 unit
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Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance of 120 m. Which of the following statements is correct?
1. The balls can never meet.
2. The balls can meet if the ball B is thrown 1 s later.
3. The two balls meet at a height of 45 m.
4. None of the above
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A body is projected at an angle of with the horizontal with a speed of 30 m/s. What is the angle made by the velocity vector with the horizontal after 1.5 sec? (g = 10)
1.
2.
3.
4.
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A particle moves along the positive branch of the curve \(y= \frac{x^{2}}{2}\) where \(x= \frac{t^{2}}{2}\), & \(x\) and \(y\) are measured in metres and in seconds respectively. At \(t= 2~\text{s}\), the velocity of the particle will be:
1. \(\left(\right. 2 \hat{i} - 4 \hat{j})~\text{m/s}\)
2. \(\left(\right. 4 \hat{i} + 2 \hat{j}\left.\right)\text{m/s}\)
3. \(\left(\right. 2 \hat{i} + 4 \hat{j}\left.\right) \text{m/s}\)
4. \(\left(\right. 4 \hat{i} - 2 \hat{j}\left.\right) \text{m/s}\)
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A deer wants to save her life from a lion. The lion follows a path whose equation is . For saving her life, the deer needs to move on a path whose equation will be:
1.
2.
3.
4. Both (1) and (3) are correct
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A particle rotates in a circular path starting from rest. If angular acceleration is 4 , then the time after which angle between net acceleration and tangential acceleration becomes
1. | 0.5 s | 2. | 0.25 s |
3. | 2 s | 4. | 4 s |
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An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at x = –2 m, its velocity is –(4 m/s). What is the object's acceleration when it is at y = 2 m?
1.
2.
3.
4.
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To the captain of a ship A travelling with velocity km/h, a second ship B appears to have a velocity km/h. What is the true velocity of the ship B?
1.
2.
3.
4. none of these
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A particle has an initial velocity m/s and it is moving with an acceleration . Velocity of the particle at \(t=2\) s will be:
1.
2.
3.
4.
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