Acceleration in 2D
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Q. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a=k2rt2, where k is a constant. The power delivered to the particle by the force acting on it at time t is given as
- Zero
- mk2r2t
- mk2rt
- mk2r2t2
Q. Column-IColumn-II(i) For a particle moving in a circle(a) The accleration may be perpendicular to its velocity(ii) For a particle moving in a straight line(b) The acceleration may be in the direction of velocity(iii) For a particle undergoing projectile motion with angle of projection α;0≤α≤π2(c) The acceleration may be at some angle θ(0≤θ≤π2)with the velocity(iv) For a particle is moving in space(d) The acceleration may be opposite to velocity
- i-a, b, ii-b, iii-a, c, iv-a, b, c, d
- i-a, c, ii-b, d iii-a, c, iv-a, b, c, d
- i-a, b, ii-b iii-a, c, iv-a, b, c, d
- i-a, b, ii-b, d iii-a, c, iv-a, b, c, d
Q. A body, starting from rest, attains a velocity of (2i+4j) m/s in 2 s. Its average acceleration is
- (i + 2j) m/s/s
- (2i + 4j) m/s/s
- (2i + j) m/s/s
- (4i + 2j) m/s/s
Q. The x and y co-ordinates of a particle at any time are x=5t2−3t+6 and y=10t2+2t+3 respectively, where x and y are in meters and t in seconds. Find the acceleration of the particle at t=1s.
- (10^i+10^j) m/s2
- (10^i+20^j) m/s2
- (20^i+10^j) m/s2
- (10^i−20^j) m/s2
Q. The coordinates of a particle moving in a plane are given by x(t) = a cos (pt) and y(t) = b sin (pt) where a, b (<a) and p are positive constants of appropriate dimensions. Then
- the path of the particle is an ellipse
- the velocity and acceleration of the particle are normal to each other at t=π/(2p)
- the acceleration of the particle is always directed towards a focus
- the distance travelled by the particle in time interval t=0tot=π/(2p) is a
Q. Column-IColumn-II(i) For a particle moving in a circle(a) The accleration may be perpendicular to its velocity(ii) For a particle moving in a straight line(b) The acceleration may be in the direction of velocity(iii) For a particle undergoing projectile motion with angle of projection α;0≤α≤π2(c) The acceleration may be at some angle θ(0≤θ≤π2)with the velocity(iv) For a particle is moving in space(d) The acceleration may be opposite to velocity
- i-a, b, ii-b, iii-a, c, iv-a, b, c, d
- i-a, c, ii-b, d iii-a, c, iv-a, b, c, d
- i-a, b, ii-b iii-a, c, iv-a, b, c, d
- i-a, b, ii-b, d iii-a, c, iv-a, b, c, d
Q. For an X-Y plot of a body undergoing 2D motion, the direction of instantaneous acceleration is always in the direction of change of velocities.
- False
- True
Q. A particle moves along the parabolic path x=y2+2y+2 in such a way that the y− component of velocity vector remains 5 ms−1 during the motion. The magnitude of the acceleration of the particle (in ms−2) is
Q. The x and y coordinates of a body are
x(t)=3t+2
y(t) =4t
What is the acceleration of the body at t=1s?
x(t)=3t+2
y(t) =4t
What is the acceleration of the body at t=1s?
- \N
- 3i + 4j
- 7i + 2j
- None of these