The magnitude of a vector is constant but it is changing its direction continuously. The angle between and is:
1. 180°
2. 120°
3. 90°
4. 0°
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) |
Assertion: | The maximum height of a projectile is always \(25\)% of the maximum range. |
Reason: | For maximum height, the projectile should be projected at \(90^\circ.\) |
1. | Both assertion and reason are correct, reason is the correct explanation of Assertion. |
2. | Both assertion and reason are correct but the reason is not the correct explanation of the assertion. |
3. | Assertion is correct and the reason is incorrect. |
4. | Assertion is incorrect and the reason is correct. |
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. |
A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0 ĵ ) . What is the speed of the particle at the instant its x-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 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0ĵ ) . What is the y-coordinate of the particle at the instant its x-coordinate is 84 m?
1. 36 m
2. 26 m
3. 1 m
4. 0 m