1

IIT-JEE 1999 Screening

MCQ (More than One Correct Answer)
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 approprite dimensions. Then
A
the path of the particle is an ellipse
B
the velocity and acceleration of the particle are normal to each other at t = $${\pi \over {2p}}$$
C
the acceleration of the particle is always directed towards a focus
D
the distance traveled by the particle in time interval t = 0 to t = $${\pi \over {2p}}$$ is a
2

IIT-JEE 1993

MCQ (More than One Correct Answer)
A particle of mass m moves on the x-axis as follows: it starts from rest at t = 0 from the point x = 0, and come to rest at t = 1 at the point x = 1. NO other information is available about its motion at intermediate times ( 0 < t < 1 ). If $$\alpha $$ denotes the instantaneous acceleration of the particle, then:
A
$$\alpha $$ cannot remain positive for all t in the interval $$0 \le t \le 1$$
B
$$\left| \alpha \right|$$ cannot exceed 2 at any point in its path.
C
$$\left| \alpha \right|$$ must be $$ \ge $$ 4 at some point or points in its path.
D
$$\alpha $$ must be change sign during the motion, but no other assertion can be made with the information given.
3

IIT-JEE 1982

MCQ (More than One Correct Answer)
A particle is moving eastwards with a velocity of 5 m/s. In 10s the velocity changes to 5 m/s northwards. The average acceleration in this time is
A
zero
B
$${1 \over {\sqrt 2 }}m/{s^2}$$ towards north-west
C
$${1 \over {\sqrt 2 }}m/{s^2}$$ towards north-east
D
$${1 \over 2}m/{s^2}$$ towards north

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