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 + bt^{2 }where a = 15 cm and b = 3 cm/sec^{2}. Its acceleration at time 3 sec will be :-

(1) 36 cm/sec^{2}

(2) 18 cm/sec^{2}

(3) 6 cm/sec^{2}

(4) 32 cm/sec^{2}

03:- Equation of displacement for a particle is s = 3t^{3 }+ 7t^{2 }+ 14t + 8 m. Its acceleration at time t = 2 sec is :-

(1) 10 m/s^{2}

(2) 16 m/s^{2}

(3) 25 m/s^{2}

(4) 50 m/s^{2}

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 = 3t^{2 }+ 5t^{3 }+ 7

(3) v = 9t^{2 }+ 8

(4) v = 4t^{–2 }+ 3t–1

07:- The displacement of a particle starting from rest (at t = 0) is given by s = 6t^{2 }– t^{3} . 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 = t^{3 }– 6t^{2 }+ 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 + bt^{2 }– ct^{3 }where a, b and c are constants. The velocity of the particle when its acceleration is zero is given by :-

(1) a + b^{2}/c

(2) a + b^{2 }/2c

(3) a + b^{2} /3c

(4)a + b^{2} /4c

10:- A particle moves along a straight line such that its displacement at any time t is given by s = (t^{3 }– 6t^{2} + 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 = at^{2 }– bt^{3}. 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 – t^{3 }where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

(1) 24 m/s^{2}

(2) zero

(3) 6 m/s^{2}

(4) 12 m/s^{2}