Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

(1)

t=x+3x=t-32At t=0 sec, x1=9mAt t=6 sec, x2=9mDisplacement=x2-x1=0

Difficulty Level:

  • 60%
  • 13%
  • 14%
  • 15%

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

Difficulty Level:

  • 22%
  • 11%
  • 65%
  • 3%

 

A point moves in a straight line under the retardation av2. If the initial velocity is u, the distance covered in 't' seconds is-

1.  aut

2.  1aln aut

3.  1aln 1+aut

4.  a ln aut

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

Difficulty Level:

  • 16%
  • 24%
  • 56%
  • 6%

A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by (4t32t), where t is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 m from the origin ?

(1) 28 m/s2

(2) 22 m/s2

(3) 12 m/s2

(4) 10 m/s2

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

(2) v=4t32t(given) ∴ a=dvdt=12t22

and x=0tvdt=0t(4t32t)dt=t4t2

When particle is at 2m from the origin t4t2=2

t4t22=0(t22)(t2+1)=0t=2sec

Acceleration at t=2sec given by,

a=12t22=12×22 = 22m/s2  

Difficulty Level:

  • 13%
  • 67%
  • 14%
  • 9%

The initial velocity of a particle is u (at t = 0) and the acceleration f is given by at. Which of the following relation is valid 

(1) v=u+at2

(2) v=u+at22

(3) v=u+at

(4) v = u

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

(2) If acceleration is variable (depends on time) then

a=dvdtdv = adt   uvdv    =0tftdt

v=u+at22

Difficulty Level:

  • 27%
  • 26%
  • 31%
  • 19%

The velocity of a body depends on time according to the equation v=20+0.1t2. The body is undergoing 

(1) Uniform acceleration

(2) Uniform retardation

(3) Non-uniform acceleration

(4) Zero acceleration

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

(3) Acceleration a=dvdt=0.1×2t=0.2t

Which is time dependent i.e. non-uniform acceleration.  

Difficulty Level:

  • 30%
  • 8%
  • 60%
  • 5%

A rocket is fired upward from the earth's surface such that it creates an acceleration of 19.6 m/sec2. If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be [MP PET 1995]

(1) 245 m

(2) 490 m

(3) 980 m

(4) 735 m

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

(4) Given a=19.6m/s2=2g

Resultant velocity of the rocket after 5 sec

v=2g×5=10gm/s

Height achieved after 5 sec, h1=12×2g×25=245m

On switching off the engine it goes up to height h2 where its velocity becomes zero.

0=(10g)22gh2h2=490m

∴ Total height of rocket =245+490=735m 

Difficulty Level:

  • 29%
  • 22%
  • 8%
  • 42%

A balloon starts rising from the ground with an acceleration of 1.25 m/s2 . After 8s, a stone is released from the balloon. The stone will (g = 10 m/s2

(1) Reach the ground in 4 second

(2) Begin to move down after being released

(3) Have a displacement of 50 m

(4) Cover a distance of 40 m in reaching the ground

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

(1)

When the stone is released from the balloon. Its height h=12at2=12×1.25×(8)2=40m and velocity

v=at=1.25×8=10m/s

Time taken by the stone to reach the ground:h=ut+12at2-40=10t+12(-10)t2t2-2t-8=0(t-4)(t+2)=0t=4sec

Difficulty Level:

  • 50%
  • 18%
  • 15%
  • 19%

The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity v0 The distance travelled by the particle in time t will be 

(1) v0t+13bt2

(2) v0t+13bt3

(3) v0t+16bt3

(4) v0t+12bt2

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

(3) dvdt=btdv=btdtv=bt22+K1

At t=0,v=v0K1=v0

We get v=12bt2+v0

Again dxdt=12bt2+v0x=12bt23+v0t+K2

At t=0,x=0K2=0

 x=16bt3+v0t 

Difficulty Level:

  • 6%
  • 21%
  • 49%
  • 26%

The acceleration of a particle starting from rest, varies with time according to the relation A = – 2 sinω t. The displacement of this particle at a time t will be

(1) 12(aω2sinωt)t2

(2) aωsinωt

(3) aωcosωt

(4) asinωt  

Concept Videos :-

#42 Non Uniform Acceleration
#43 Solved Examples 29
#44 Solved Examples 30

Concept Questions :-

Non-uniform acceleration

(4) Velocity v=Adt=(aω2sinωt)dt=aωcosωt

Displacement x =vdt=aωcosωtdt=asinωt   

Difficulty Level:

  • 20%
  • 17%
  • 14%
  • 50%