Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be 

(1)$\frac{t_1-t_2}{2}$

(2)$\frac{t_1{t}_2}{t_2-t_1}$

(3) $\frac{t_1{t}_2}{t_2+t_1}$

(4) $t_1-t_2$

The x and y coordinates of the particle at any time are $\mathrm{x}=$ $5\mathrm{t}-2{\mathrm{t}}^2$ and \(\mathrm{y}=10\mathrm{t}\) respectively, where x and y are in meters and \(\mathrm{t}\) in seconds. The acceleration of the particle at \(\mathrm{t}=2\) s is:
1. \(5\hat{i}\) $\mathrm{m}/{\mathrm{s}}^2$

2. \(-4\hat{i}\) $\mathrm{m}/{\mathrm{s}}^2$

3. \(-8\hat{j}\) $\mathrm{m}/{\mathrm{s}}^2$

4. \(0\)

A particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant.  Based on the information given, which of the following is true?

A particle of mass 10g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8x10^-4 J by the end of the second revolution after the beginning of the motion?

(1) 0.15 m/s²

(2) 0.18 m/s²

(3) 0.2 m/s²

(4) 0.1 m/s²

In the given figure, \(a=15\) m /s² represents the total acceleration of a particle moving in the clockwise direction in a circle of radius \(R=2.5\) m at a given instant of time. The speed of the particle is:

             

1. \(4.5\) m/s
2. \(5.0\) m/s
3. \(5.7\) m/s
4. \(6.2\) m/s