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): | 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): | 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. Choose the incorrect statement(s):
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. | \(a_{avg}=\frac{v(t_{2})-v(t_{1})}{t_{2}-t_{1}}\) |
1. | (a), (d) |
2. | (a), (c) |
3. | (b), (c) |
4. | (a), (b) |
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) 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 \(84\) m?
1. | \(36\) m/s | 2. | \(26\) m/s |
3. | \(1\) m/s | 4. | \(0\) m/s |
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i\) 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-coordinate of the particle at the instant its \(x\text-\)coordinate is \(84\) m?
1. \(36\) m
2. \(26\) m
3. \(1\) m
4. \(0\) m