Curvilinear Motion

Q. Starting from rest, a particle moves along a circular path of radius 1 m so that the distance travelled is given by the expression $s=2t^2+c$ where c is a constant. The tangential acceleration of the particle (in m/s${}^2$) is

1. 2
2. 4
3. 6
4. 8

Q. To an observer standing on the ground the velocity of a cyclist is 12 m/s in the horizontal direction and that or rain drops falling vertically down is 6 m/s. The magnitude of the velocity of the rain drops relative to the cyclist is

1. 6 m/s
2. 12 m/s
3. 13.4 m/s
4. 18.4 m/s

Q. Figure below shows a particle sliding on a frictionless track which terminates in a straight horizontal section. If the particle starts slipping from the point A, how far away from the end of track will the particle hit the ground? Assume, $g=10\frac{m}{s^2}$

1. $2m$
2. $3m$
3. $4m$
4. $1m$