In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
1. | The acceleration of the particle is zero. |
2. | The acceleration of the particle is increasing. |
3. | The acceleration of the particle is necessarily in the plane of motion. |
4. | The particle must be undergoing a uniform circular motion. |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyThe position vector of a particle \(\overrightarrow r\) as a function of time \(t\) (in seconds) is \(\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}\). The initial acceleration of the particle is:
1. \(2~\text{m/s}^2\)
2. \(3~\text{m/s}^2\)
3. \(4~\text{m/s}^2\)
4. zero
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyThe \(x\) 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. | \(0\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA body is moving with a velocity of \(30\) m/s towards the east. After \(10\) s, its velocity becomes \(40\) m/s towards the north. The average acceleration of the body is:
1. \( 7~\text{m/s}^2\)
2. \( \sqrt{7}~\text{m/s}^2\)
3. \(5~\text{m/s}^2\)
4. \(1~\text{m/s}^2\)
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyIf the position of a particle varies according to the equations \(x= 3t^2\), \(y =2t\), and \(z= 4t+4\), then which of the following is incorrect?
1. | Velocities in \(y\) and \(z\) directions are constant |
2. | Acceleration in the \(x\text-\)direction is non-uniform |
3. | Acceleration in the \(x\text-\)direction is uniform |
4. | Motion is not in a straight line |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA particle is moving in the XY plane such that \(x = \left(t^2 -2t\right)\) m, and \(y = \left(2t^2-t\right)\) m, then:
1. | Acceleration is zero at \(t=1\) sec. |
2. | Speed is zero at \(t=0\) sec. |
3. | Acceleration is always zero. |
4. | Speed is \(3\) m/s at \(t=1\) sec. |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant. Based on the information given, which of the following is true?
1. | Velocity and acceleration, both are parallel to \(r\). |
2. | Velocity is perpendicular to \(r\) and acceleration is directed towards the origin. |
3. | Velocity is not perpendicular to \(r\) and acceleration is directed away from the origin. |
4. | Velocity and acceleration, both are perpendicular to \(r\). |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA particle moves in space such that:
\(x=2t^3+3t+4;~y=t^2+4t-1;~z=2\sin\pi t\)
where \(x,~y,~z\) are measured in meters and \(t\) in seconds. The acceleration of the particle at \(t=3\) seconds will be:
1. | \(36 \hat{i}+2 \hat{j}+\hat{k} \) ms-2 |
2. | \(36 \hat{i}+2 \hat{j}+\pi \hat{k} \) ms-2 |
3. | \(36 \hat{i}+2 \hat{j} \) ms-2 |
4. | \(12 \hat{i}+2 \hat{j} \) ms-2 |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA particle moving on a curved path possesses a velocity of \(3\) m/s towards the north at an instant. After \(10\) s, it is moving with speed \(4\) m/s towards the west. The average acceleration of the particle is:
1. | \(0.25~\text{m/s}^2,\) \(37^{\circ}\) south to east. |
2. | \(0.25~\text{m/s}^2,\) \(37^{\circ}\) west to north. |
3. | \(0.5~\text{m/s}^2,\) \(37^{\circ}\) east to north. |
4. | \(0.5~\text{m/s}^2,\) \(37^{\circ}\) south to west. |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA 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. |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & Biology