Q. No.The position of an object moving along the x-axis is given by, \(x=a+bt^2\) where \(a=8.5\) m, \(b=2.5\) ms-2, and \(t\) is measured in seconds. Its velocity at \(t=2.0\) s will be:
1. \(13\) m/s
2. \(17\) m/s
3. \(10\) m/s
4. \(0\)
1. \(13\) m/s
2. \(17\) m/s
3. \(10\) m/s
4. \(0\)
When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity \(\mathrm{v_0}\) and the braking capacity, or deceleration, \(-a\) that is caused by the braking. Expression for stopping distance of a vehicle in terms of \(\mathrm{v_0}\) and \(a\) is:
1. \(\frac{\mathrm{v_o}^2}{2a}\)
2. \(\frac{\mathrm{v_o}}{2a}\)
3. \(\frac{\mathrm{v_o}^2}{a}\)
4. \(\frac{2a}{\mathrm{v_o}^2}\)
If a body travels some distance in a given time interval, then for that time interval, its:
| 1. | Average speed ≥ |Average velocity| |
| 2. | |Average velocity| ≥ Average speed |
| 3. | Average speed < |Average velocity| |
| 4. | |Average velocity| must be equal to average speed. |
The displacement \(x\) of a particle varies with time \(t\) as \(x = ae^{-\alpha t}+ be^{\beta t}\)
, where \(a,\) \(b,\) \(\alpha,\) and \(\beta\) are positive constants. The velocity of the particle will:
| 1. | be independent of \(\alpha\) and \(\beta.\) |
| 2. | go on increasing with time. |
| 3. | drop to zero when \(\alpha=\beta.\) |
| 4. | go on decreasing with time. |
The figure shows the displacement-time graph of a particle moving on the x-axis. Then,
| 1. | the particle is continuously going in a positive x-direction. |
| 2. | the particle is at rest. |
| 3. | the velocity increases up to a time \(t_0\), and then becomes constant. |
| 4. | the particle moves at a constant velocity up to a time \(t_0\), and then stops. |
A stone is released from an elevator going up with an acceleration \(a.\) The acceleration of the stone after the release is:
1. \(a\) upward
2. \((g-a)\) upward
3. \((g-a)\) downward
4. \(g\) downward
Mark the correct statements for a particle going on a straight line:
| a. | if the velocity and acceleration have opposite sign, the object is slowing down. |
| b. | if the position and velocity have opposite sign, the particle is moving towards the origin. |
| c. | if the velocity is zero at an instant, the acceleration should also be zero at that instant. |
| d. | if the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval. |
Choose the correct option:
| 1. | (a), (b) and (c) |
| 2. | (a), (b) and (d) |
| 3. | (b), (c) and (d) |
| 4. | all of these |
A boy throws a ball straight up the side of a building and receives it after \(4\) s. On the other hand, if he throws it so that it strikes a ledge on its way up, it returns to him after \(3\) s. The ledge is at a distance \(d\) below the highest point, where \(d=?\) (take acceleration due to gravity, \(g=10\) m/s2)
1. \(5\) m
2. \(2.5\) m
3. \(1.25\) m
4. \(10\) m
| 1. | statics | 2. | kinematics |
| 3. | mechanics | 4. | dynamics |
| 1. | Both cannot be zero. |
| 2. | One of the two may be zero. |
| 3. | Both must be zero. |
| 4. | If one is positive, the other is negative, and vice-versa. |
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