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
A 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. | The velocity and acceleration, both are parallel to \(r.\) |
2. | The velocity is perpendicular to \(r\) and acceleration is directed towards the origin. |
3. | The velocity is not perpendicular to \(r\) and acceleration is directed away from the origin. |
4. | The velocity and acceleration, both are perpendicular to \(r.\) |
A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards north. The average acceleration of the body is
(1)
(2)
(3)
(4)
A 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 |
If 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 |