The displacement of particle is given by X = a_o + \(\frac{a_1t}{2}-\frac{2_2t^2}{3}\) What is its acceleration?

(a)

\(\frac{2a_2}{3}\)

(b)

\(-\frac{2a_2}{3}\)

(c)

a₂

(d)

zero

The slope of the velocity-time graph for retarded motion is ______________

(a)

positive

(b)

negative

(c)

zero

(d)

can be positive, negative or zero

The path of a particle moving under the influence of a force fixed in magnitude and direction is ______________

(a)

straight line

(b)

circle

(c)

parabola

(d)

ellipse

A train is moving towards east and a car is along north, both with same speed. The passenger in the train is observed the car moving in which of the following direction?

(a)

East-north direction

(b)

West-north direction

(c)

South-east direction

(d)

None of these

A man should hold his umbrella with vertical, when rain falls vertically with velocity \(\vec { { V }_{ R } } \) and man walks horizontally with velocity \(\vec{{V}_{M}}\) is _____________

(a)

\(tan^{-1}(\frac{\vec{V}_{M}}{\vec{V}_{R}})\)

(b)

\(tan^{-1}(\frac{\vec{V}_{R}}{\vec{V}_{M}})\)

(c)

tan^-1(V_R)

(d)

tan^-1(V_M)