1. | \(42\) m | 2. | \(47\) m |
3. | \(19\) m | 4. | \(40\) m |
Assertion (A): | Uniform circular motion is the only example of a situation in which the speed of a particle remains constant even though a force is acting on the particle. |
Reason (R): | In uniform circular motion, a force acting along the circle pushes the particle forward. |
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. |
Assertion (A): | For a given initial and final position the average velocity is single-valued while the average speed can have many values. |
Reason (R): | Velocity is a vector quantity and speed is a scalar quantity. |
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. |
Assertion (A): | The maximum height of a projectile is always \(25\)% of the maximum range. |
Reason (R): | For maximum height, the projectile should be projected at \(90^\circ.\) |
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 and (R) is False. |
4. | (A) is False and (R) is True. |
The magnitude of vector \(\vec{A}\) is constant but it is changing its direction continuously. The angle between \(\vec {A}\) and \(\frac{d \vec{A}}{dt}\) is:
1. \(180^\circ\)
2. \(120^\circ\)
3. \(90^\circ\)
4. \(0^\circ\)
The following are four different relations about displacement, velocity, and acceleration for the motion of a particle in general.
(a) | \(v_{avg}=\frac{1}{2} [ v(t_{1})+v(t_{2}) ]\) |
(b) | \(v_{avg}=\frac{r(t_{2})-r(t_{1})}{t_{2}-t_{1}}\) |
(c) | \(r=\frac{1}{2}[ v(t_{2})-v(t_{1}) ](t_2-t_1)\) |
(d) | \(a_{avg}=\frac{v(t_{2})-v(t_{1})}{t_{2}-t_{1}}\) |
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i~\text{m/s}\) and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0\hat j)~\text{m/s}^2.\) What is the speed of the particle at the instant its \(x\text-\)coordinate is \(84~\text m?\)
1. \(36~\text{m/s}\)
2. \(26~\text{m/s}\)
3. \(1~\text{m/s}\)
4. Zero
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i~\text{m/s}\) and moves in the \({x\text -y}\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0 \hat j)~\text{m/s}^2.\) What is the \({y\text -}\)coordinate of the particle at the instant its \({x\text -}\)coordinate is \(84~\text m?\)
1. \(36~\text m\)
2. \(26~\text m\)
3. \(1~\text m\)
4. Zero