Motion in A Plane

A particle starting from the origin (0,0) moves in a straight line in the (x,y) plane. Its coordinates at a later time are  ( ). The path of the particle makes with the x -axis an angle of:

• 30^o

• 45^o C

• 60^o C

• 60^o C

A car moves from X to Y with a uniform speed v_u and returns to Y with a uniform speed v_d. The average speed for this round trip is:

• 60^o

• 45^o

• 30^o

• 30^o

A particle moving along x- axis has acceleration f, at time t, given f = f_o (1-t/T), where f_o and T are constants. The particle at t =0 and the instant when f = 0, the particle's velocity (v_x) is:

• f_oT

• f_oT²/2

• f_oT²

• f_oT²

For angles of projection of a projectile at angles (45° - θ) and (45° + θ), the horizontal ranges described by the projectile are in the ratio of

• 1:1

• 2:3

• 1:2

• 1:2

A car runs at aconstant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap respectively is

• 0, 0

• 0, 10 m/s

• 10 m/s,  10m/s

• 10 m/s,  10m/s

The vectors  are such that a:

The  angle between the two vectors is

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk up on the moving escalator will be

The moment of the force, at (2, 0, 3) about the point (2,-2,2), is given by

A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are t₁ and t₂, respectively.

• $\frac{\mathrm{g}\sqrt{{\mathrm{t}}_1{\mathrm{t}}_2}}{2}$

• $\frac{\mathrm{g}({\mathrm{t}}_1 +{\mathrm{t}}_2)}{2}$

• $\mathrm{g}\sqrt{{\mathrm{t}}_1{\mathrm{t}}_2}$

• $\mathrm{g}\frac{{\mathrm{t}}_1{\mathrm{t}}_2}{({\mathrm{t}}_1+{\mathrm{t}}_2)}$