XI-Unit: : 02 :: Motion in straight line -Paper no-01

Hello students . Today’s assignment (19/06/2023) for kinematics   based on calculus .

01:- If x denotes displacement in time t and x = a sin t, then acceleration is :
(1) a cos t
(2) –a cos t
(3) a sin t
(4) –a sin t

02:- The motion of a particle is described by the equation x = a + bt² where a = 15 cm and b = 3 cm/sec². Its acceleration at time 3 sec will be :-
(1) 36 cm/sec²
(2) 18 cm/sec²
(3) 6 cm/sec²
(4) 32 cm/sec²

03:- Equation of displacement for a particle is s = 3t³ + 7t² + 14t + 8 m. Its acceleration at time t = 2 sec is :-
(1) 10 m/s²
(2) 16 m/s²
(3) 25 m/s²
(4) 50 m/s²

04:- If for a particle position x ∝t  then :–
(1) velocity is constant
(2) acceleration is non zero
(3) acceleration is variable
(4) none of these

05:- The velocity of a body depends on time according to the equation v = 20 + 0.1t. The body has :
(1) uniform acceleration
(2) uniform retardation
(3) non-uniform acceleration
(4) zero acceleration

06:- Which of the following relations representing velocity of a particle describes motion with constant acceleration?
(1) v = 6 – 7t
(2) v = 3t² + 5t³ + 7
(3) v = 9t² + 8
(4) v = 4t^–2 + 3t–1

07:- The displacement of a particle starting from rest (at t = 0) is given by s = 6t² – t³ . The time when the particle will attain zero acceleration is :
(1) 2s
(2) 8s
(3) 12s
(4) 16s

08:-  A particle moves along a straight line such that its displacement at any time t is given by s = t³ – 6t² + 3t + 4 metres. The displacement when the acceleration is zero is :-
(1) 3 m
(2) –12 m
(3) 42 m
(4) –6 m

09:- Displacement x of a particle is related to time t as x = at + bt² – ct³ where a, b and c are constants. The velocity of the particle when its acceleration is zero is given by :-
(1) a +  b²/c
(2) a + b² /2c
(3) a + b² /3c
(4)a + b² /4c

10:- A particle moves along a straight line such that its displacement at any time t is given by s = (t³ – 6t² + 3t + 4) metres. The velocity when the acceleration is zero is

(1) 3 m/s
(2) –15 m/s
(3) 42 m/s
(4) – 9 m/s

11:- The position x of a particle varies with time, (t) as x = at² – bt³. The acceleration will be zero at time t is equal to

(1) a/3b
(2) zero
(3) 2a/3b
(4) a/b

12:- The motion of a particle along a straight line is described by equation x = 8 + 12t – t³ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is 

(1) 24 m/s²
(2) zero
(3) 6 m/s²
(4) 12 m/s²