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 |
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. \(\frac{2a}{\mathrm{v_o}^2}\)
A particle moves a distance \(x\) in time \(t\) according to equation \(x=(t+5)^{-1}.\) The acceleration of the particle is proportional to:
1. (velocity)\(3/2\)
2. (distance)\(2\)
3. (distance)\(-2\)
4. (velocity)\(2/3\)
1. | zero |
2. | constant |
3. | proportional to time |
4. | proportional to displacement |