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Q. No.A Cheetah can accelerate from \(0\) to \(96\) km/h in \(2\) s. What is the average acceleration of the Cheetah?
1. \(10\) m/s2
2. \(13.3\) m/s2
3. \(15\) m/s2
4. \(48\) m/s2
| 1. | \(\dfrac{5}{3}\) m/s | 2. | \(\dfrac{4}{3}\) m/s |
| 3. | \(2\) m/s | 4. | \(3\) m/s |
Then its acceleration varies as:
| 1. | \(\dfrac{1}{\sqrt x}\) | 2. | \(x^{3/2}\) |
| 3. | \(x^{-3/2}\) | 4. | \(x^0\) |
| (a) | \(x(t)>0\) for all \(t>0\) |
| (b) | \(v(t)>0\) for all \(t>0\) |
| (c) | \(a(t)>0\) for all \(t>0\) |
| (d) | \(v(t)\) lies between \(0\) and \(2\) |
Choose the correct option:
1. (a), (c)
2. (b), (c)
3. (a), (d)
4. (b), (d)
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 lift is coming from the \(8\)th floor and is just about to reach the \(4\)th floor. Taking the ground floor as the origin and positive direction upwards for all quantities, which one of the following is correct:
| 1. | \(x>0, v<0, a>0\) |
| 2. | \(x>0, v<0, a<0\) |
| 3. | \(x<0, v<0, a<0\) |
| 4. | \(x>0, v>0, a<0\) |
The figure gives a speed-time graph of a particle in motion along the same direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude?
| 1. | Interval 2 | 2. | Interval 1 |
| 3. | Interval 3 | 4. | Equal in all intervals |
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 \({v_0}\) and the braking capacity, or deceleration, \(-a\) that is caused by the braking. Expression for stopping distance of a vehicle in terms of \({v_0}\) and \(a\) is:
| 1. | \(\dfrac{{v_o}^2}{2a}\) | 2. | \(\dfrac{{v_o}}{2a}\) |
| 3. | \(\dfrac{{v_o}^2}{a}\) | 4. | \(\dfrac{2a}{{v_o}^2}\) |
If a particle has negative velocity and negative acceleration, its speed:
1. increases
2. decreases
3. remains the same
4. zero
A particle in one-dimensional motion:
| 1. | with zero speed at an instant may have non-zero acceleration at that instant. |
| 2. | with zero speed may have non-zero velocity. |
| 3. | with constant speed, must have non-zero acceleration. |
| 4. | with a positive value of acceleration must be speeding up. |
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Q. No.
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