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Q. No.A particle is moving along a curve. Select the correct statement.
| 1. | If its speed is constant, then it has no acceleration. |
| 2. | If its speed is increasing, then the acceleration of the particle is along its direction of motion. |
| 3. | If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. |
| 4. | If its speed is constant, its acceleration is perpendicular to its velocity. |
The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^2\) and \({y}=10{t}\) respectively, where \(x\) and \(y\) are in meters and \(\mathrm{t}\) in seconds. The acceleration of the particle at \(\mathrm{t}=2\) s is:
| 1. | \(5\hat{i}~\text{m/s}^2\) | 2. | \(-4\hat{i}~\text{m/s}^2\) |
| 3. | \(-8\hat{j}~\text{m/s}^2\) | 4. | \(0\) |
A particle is moving in the \(XY\) plane such that \(x = \left(t^2 -2t\right)~\text m,\) and \(y = \left(2t^2-t\right)~\text m,\) then:
| 1. | the acceleration is zero at \(t=1~\text s.\) |
| 2. | the speed is zero at \(t=0~\text s.\) |
| 3. | the acceleration is always zero. |
| 4. | the speed is \(3~\text{m/s}\) at \(t=1~\text s.\) |
In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then, which of the following is necessarily true?
| 1. | the average velocity is not zero at any time. |
| 2. | average acceleration must always vanish. |
| 3. | displacements in equal time intervals are equal. |
| 4. | equal path lengths are traversed in equal intervals. |
The \(x\) and \(y\) coordinates of the particle at any time are \(x = 5t-2t^2\) and \(y=10t\) respectively, where \(x\) and \(y\) are in metres and \(t\) is in seconds. The acceleration of the particle at \(t=2\) s is:
1. \(0\) m/s2
2. \(5\) m/s2
3. \(-4\) m/s2
4. \(-8\) m/s2
| Assertion (A): | In a two-dimensional motion, there are two accelerations acting on the particle. |
| Reason (R): | Both the components of velocity, i.e., horizontal and vertical, in case of free fall keeps on changing with respect to time. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
| 1. | \(5\sqrt2\) m/s2 SE | 2. | \(\dfrac{5}{\sqrt2}\) m/s2 SE |
| 3. | \(5\sqrt2\) m/s2 NE | 4. | \(\dfrac{5}{\sqrt2}\) m/s2 NE |
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Q. No.
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