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Q. No.A ball \((A)\) is projected vertically upward, a second ball \((B)\) is projected horizontally with the same initial speed as the first. The relative velocity of ball \(A\) with respect to \(B\):
| 1. | is constant in magnitude only. |
| 2. | is constant in direction. |
| 3. | is constant in magnitude and direction. |
| 4. | varies, both, in magnitude and direction. |
Subtopic: Relative Motion in One Dimension |
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A ball, thrown vertically upward, is observed to move upward with a speed \(v_1\) at time \(t_1\) and a speed \(v_2,\) downward, at time \(t_2.\)
The acceleration of the ball is (downward):
1. \(\dfrac{v_2-v_1}{t_2-t_1}\)
2. \(\dfrac{v_2+v_1}{t_2-t_1}\)
3. \(\dfrac{v_2-v_1}{t_2+t_1}\)
4. \(\dfrac{v_2+v_1}{t_2+t_1}\)
The acceleration of the ball is (downward):
1. \(\dfrac{v_2-v_1}{t_2-t_1}\)
2. \(\dfrac{v_2+v_1}{t_2-t_1}\)
3. \(\dfrac{v_2-v_1}{t_2+t_1}\)
4. \(\dfrac{v_2+v_1}{t_2+t_1}\)
Subtopic: Acceleration |
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A ball is dropped vertically from height \(h\) and bounces elastically on the floor (see figure). Which of the following plots best depicts the acceleration of the ball as a function of time?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Uniformly Accelerated Motion |
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Two cars \(A\) and \(B\) start moving along the same straight road, from the same point, simultaneously. The first car \((A)\) accelerates uniformly to a maximum speed of \(v_0\) and then decelerates uniformly to a stop. The second car \((B)\) accelerates uniformly to the same maximum speed \(v_0\) and then decelerates uniformly to a stop. The acceleration of \(A\) is twice that of \(B,\) and they both spend the same total time during the motion. Then,
Choose the correct option from the given ones:
| (A) | distance travelled by \(A\) = distance travelled by \(B\) |
| (B) | acceleration time of \(A\) = \(\dfrac12\) acceleration time of \(B\) |
| (C) | relative velocity of \(A\) with respect to \(B\) is always positive |
| (D) | deceleration time of \(A\) = \(2×\) deceleration time of \(B\) |
Choose the correct option from the given ones:
| 1. | (A) is True. |
| 2. | (A), (B) are True. |
| 3. | (A), (B), (C) are True. |
| 4. | (B), (C), (D) are True. |
Subtopic: Acceleration |
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The line \(AB\) makes a \(45^\circ\) angle with the \(x\)-axis, but it moves along the negative \(y\)-axis with a speed of \(1~\text{m/s}.\) The velocity, of the intersection \((C)\) of \(AB\) with \(x\)-axis, is:
| 1. | \(1~\text{m/s}\) along the positive \(x\)-axis |
| 2. | \(1~\text{m/s}\) along the negative \(x\)-axis |
| 3. | \(\dfrac{1}{\sqrt2} ~\text{m/s}\) along the positive \(x\)-axis |
| 4. | \(\dfrac{1}{\sqrt2}~\text{m/s}\) along the negative \(x\)-axis |
Subtopic: Instantaneous Speed & Instantaneous Velocity |
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In the following displacement \((x)\) versus time \((t)\) graph, at which points \(P, Q\) and \(R\) will the object's speed be increasing?
1. \(R\) only
2. \(P\) only
3. \(Q\) and \(R\) only
4. \(P,Q,R\)
Subtopic: Graphs |
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The accompanying graph of position \((x)\) versus time \((t)\) represents the motion of a particle. If \(p\) and \(q\) are both positive constants, the expression that best describes the acceleration of the particle is:
1. \(a=-p-qt\)
2. \(a=-p+qt\)
3. \(a=p+qt\)
4. \(a=p-qt\)
Subtopic: Graphs |
From NCERT
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A ball, thrown vertically upward, is observed to move upward with a speed \(v_1\) at time \(t_1\) and a speed \(v_2,\) downward, at time \(t_2.\)
The average velocity of the ball during the motion is (downward):
The average velocity of the ball during the motion is (downward):
| 1. | \(\large\frac{v_2-v_1}{2}\) | 2. | \(\large\frac{v_2+v_1}{2}\) |
| 3. | \({v_2-v_1}\) | 4. | \({v_2+v_1}\) |
Subtopic: Average Speed & Average Velocity |
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A ball is thrown vertically upward and it reaches the highest point in \(4~\text s.\) Immediately, a second ball is thrown upwards with an initial speed that is twice that of the first. The second ball meets the first after a time:
1. \(1~\text s\)
2. \(2~\text s\)
3. \(3~\text s\)
4. \(4~\text s\)
Subtopic: Relative Motion in One Dimension |
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Two cars \(A\) and \(B,\) each \(5~\text{m}\) long, are travelling along parallel lanes with speeds of \(36~\text{km/hr}\) and \(72~\text{km/hr}.\) The car \(B\) is just behind the car \(A,\) but is beginning to overtake. What will be the distance covered by the car \(B\) by the time it is just ahead of the car \(A?\)
| 1. | \(10~\text{m}\) | 2. | \(15~\text{m}\) |
| 3. | \(20~\text{m}\) | 4. | \(25~\text{m}\) |
Subtopic: Relative Motion in One Dimension |
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