01. Plane Motion Analysis
Motion in Plane

143694 The position vector of a particle is \(\vec{r}=(\operatorname{acos} \omega t) \hat{i}+(a \sin \omega t) \hat{j}\). The velocity of the particle is

1 directed towards the origin
2 directed away from the origin
3 parallel to the position vector
4 perpendicular to the position vector
Motion in Plane

143695 Speeds of two identical cars are \(u\) and \(4 u\) at a specific instant. The ratio of the respective distance in which the two cars are stopped in the same time

1 \(1: 1\)
2 \(1: 4\)
3 \(1: 8\)
4 \(1: 16\)
Motion in Plane

143696 The magnitude of acceleration and velocity of a particle moving in a plane, whose position vector \(\overrightarrow{\mathbf{r}}=\mathbf{3} \mathbf{t} \hat{\mathbf{i}}+\mathbf{2 t} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) at \(\mathbf{t}=\mathbf{2} \mathbf{s}\) are respectively

1 \(\sqrt{148,6}\)
2 \(\sqrt{144,6}\)
3 \(\sqrt{13,3}\)
4 \(\sqrt{14,3}\)
Motion in Plane

143697 A \(4 \mathrm{~kg}\) object has a velocity, \(3.0 \hat{\mathrm{i}} \mathrm{m} / \mathrm{s}\) at some instant. 8 seconds later, its velocity is \((8.0 \hat{\mathrm{i}}+10.0 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}\). Assuming that the object is subjected to a constant net force, the magnitude of the force is

1 \(\frac{5 \sqrt{5}}{2} \mathrm{~N}\)
2 \(\frac{5 \sqrt{3}}{8} \mathrm{~N}\)
3 \(\frac{8 \sqrt{5}}{3} \mathrm{~N}\)
4 \(\frac{10 \sqrt{3}}{7} \mathrm{~N}\)
Motion in Plane

143694 The position vector of a particle is \(\vec{r}=(\operatorname{acos} \omega t) \hat{i}+(a \sin \omega t) \hat{j}\). The velocity of the particle is

1 directed towards the origin
2 directed away from the origin
3 parallel to the position vector
4 perpendicular to the position vector
Motion in Plane

143695 Speeds of two identical cars are \(u\) and \(4 u\) at a specific instant. The ratio of the respective distance in which the two cars are stopped in the same time

1 \(1: 1\)
2 \(1: 4\)
3 \(1: 8\)
4 \(1: 16\)
Motion in Plane

143696 The magnitude of acceleration and velocity of a particle moving in a plane, whose position vector \(\overrightarrow{\mathbf{r}}=\mathbf{3} \mathbf{t} \hat{\mathbf{i}}+\mathbf{2 t} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) at \(\mathbf{t}=\mathbf{2} \mathbf{s}\) are respectively

1 \(\sqrt{148,6}\)
2 \(\sqrt{144,6}\)
3 \(\sqrt{13,3}\)
4 \(\sqrt{14,3}\)
Motion in Plane

143697 A \(4 \mathrm{~kg}\) object has a velocity, \(3.0 \hat{\mathrm{i}} \mathrm{m} / \mathrm{s}\) at some instant. 8 seconds later, its velocity is \((8.0 \hat{\mathrm{i}}+10.0 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}\). Assuming that the object is subjected to a constant net force, the magnitude of the force is

1 \(\frac{5 \sqrt{5}}{2} \mathrm{~N}\)
2 \(\frac{5 \sqrt{3}}{8} \mathrm{~N}\)
3 \(\frac{8 \sqrt{5}}{3} \mathrm{~N}\)
4 \(\frac{10 \sqrt{3}}{7} \mathrm{~N}\)
Motion in Plane

143694 The position vector of a particle is \(\vec{r}=(\operatorname{acos} \omega t) \hat{i}+(a \sin \omega t) \hat{j}\). The velocity of the particle is

1 directed towards the origin
2 directed away from the origin
3 parallel to the position vector
4 perpendicular to the position vector
Motion in Plane

143695 Speeds of two identical cars are \(u\) and \(4 u\) at a specific instant. The ratio of the respective distance in which the two cars are stopped in the same time

1 \(1: 1\)
2 \(1: 4\)
3 \(1: 8\)
4 \(1: 16\)
Motion in Plane

143696 The magnitude of acceleration and velocity of a particle moving in a plane, whose position vector \(\overrightarrow{\mathbf{r}}=\mathbf{3} \mathbf{t} \hat{\mathbf{i}}+\mathbf{2 t} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) at \(\mathbf{t}=\mathbf{2} \mathbf{s}\) are respectively

1 \(\sqrt{148,6}\)
2 \(\sqrt{144,6}\)
3 \(\sqrt{13,3}\)
4 \(\sqrt{14,3}\)
Motion in Plane

143697 A \(4 \mathrm{~kg}\) object has a velocity, \(3.0 \hat{\mathrm{i}} \mathrm{m} / \mathrm{s}\) at some instant. 8 seconds later, its velocity is \((8.0 \hat{\mathrm{i}}+10.0 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}\). Assuming that the object is subjected to a constant net force, the magnitude of the force is

1 \(\frac{5 \sqrt{5}}{2} \mathrm{~N}\)
2 \(\frac{5 \sqrt{3}}{8} \mathrm{~N}\)
3 \(\frac{8 \sqrt{5}}{3} \mathrm{~N}\)
4 \(\frac{10 \sqrt{3}}{7} \mathrm{~N}\)
Motion in Plane

143694 The position vector of a particle is \(\vec{r}=(\operatorname{acos} \omega t) \hat{i}+(a \sin \omega t) \hat{j}\). The velocity of the particle is

1 directed towards the origin
2 directed away from the origin
3 parallel to the position vector
4 perpendicular to the position vector
Motion in Plane

143695 Speeds of two identical cars are \(u\) and \(4 u\) at a specific instant. The ratio of the respective distance in which the two cars are stopped in the same time

1 \(1: 1\)
2 \(1: 4\)
3 \(1: 8\)
4 \(1: 16\)
Motion in Plane

143696 The magnitude of acceleration and velocity of a particle moving in a plane, whose position vector \(\overrightarrow{\mathbf{r}}=\mathbf{3} \mathbf{t} \hat{\mathbf{i}}+\mathbf{2 t} \hat{\mathbf{j}}+\hat{\mathbf{k}}\) at \(\mathbf{t}=\mathbf{2} \mathbf{s}\) are respectively

1 \(\sqrt{148,6}\)
2 \(\sqrt{144,6}\)
3 \(\sqrt{13,3}\)
4 \(\sqrt{14,3}\)
Motion in Plane

143697 A \(4 \mathrm{~kg}\) object has a velocity, \(3.0 \hat{\mathrm{i}} \mathrm{m} / \mathrm{s}\) at some instant. 8 seconds later, its velocity is \((8.0 \hat{\mathrm{i}}+10.0 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}\). Assuming that the object is subjected to a constant net force, the magnitude of the force is

1 \(\frac{5 \sqrt{5}}{2} \mathrm{~N}\)
2 \(\frac{5 \sqrt{3}}{8} \mathrm{~N}\)
3 \(\frac{8 \sqrt{5}}{3} \mathrm{~N}\)
4 \(\frac{10 \sqrt{3}}{7} \mathrm{~N}\)