In this article find kinematics questions with solutions to some selected problems.

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**Kinematics Objective type questions**

### Kinematics Numericals

1. A boy is standing at a distance a

2. A ball is thrown upward from a point on the side of a hill which slopes upward uniformly at angle 45°.Intial velocty of the ball is u

3.A cannon on a level plain is aimed at an angle θ above the horizontal.A shell is fired with a muzzle velocity v

a find the timetaken to reach the pole

b. find the value of H in terms of θ,R and v

4. The displacement of the body x(in meters) varies with time t (in sec) as

x=(-2/3)t

find following

a. what is the velocty at t=0,t=1

b. what is the acceleration at t=0

c. what is the displacement at t=0

d .what will the displacement when it comes to rest

e .How much time it take to come to rest.

5. A man runs at a speed at 4 m/s to overtake a standing bus.When he is 6 m behind the door at t=0,the bus moves forward and continues with constant acceleration of 1.2 m/s

find the following

a. how long does it take for the man to gain the door

b if in the beginning he is 10m behind the door ,will he running at the same speed ever catch up bus?

3. The time taken to reach the pole is given

R=v

or t=R/v

Now equation of motion of vertical motion

h=v

at t=R/v

so

H=(v

or H=Rtanθ-gR

4.

Given x=(-2/3)t

Velocity=dx/dt=(-4/3)t+16

so velocity at t=0 =16

and velocity at t=1 =(-4/3)+16=44/3

Acceleration is given as =d

so acceleration is time independent and it is constant

Displacement at t=0 can be found by simply substituting the values of t=0 in equation (1)

=2

Now v=(-4/3)t+16

when v=0

then t=4/3 sec

Displacement can be found by substituing the value of t=4/3 in equation (1)

=-32/27+64/3+2

=(-32+576+54)/27=598/27 m

_{1}from the foot of a tower.The boy throws an stone at a angle 45° which just touches the top of the tower and strikes the ground at a distance a_{2}from the point the boy is standing.Find the height of the tower2. A ball is thrown upward from a point on the side of a hill which slopes upward uniformly at angle 45°.Intial velocty of the ball is u

_{0}m/s and at an angle 65°(with respect to the horizotal).At what distance up the slope the ball strike and in what time?3.A cannon on a level plain is aimed at an angle θ above the horizontal.A shell is fired with a muzzle velocity v

_{0}towards a pole which is distance R away.It hits the pole at height H.a find the timetaken to reach the pole

b. find the value of H in terms of θ,R and v

_{0}4. The displacement of the body x(in meters) varies with time t (in sec) as

x=(-2/3)t

^{2}+16t+2find following

a. what is the velocty at t=0,t=1

b. what is the acceleration at t=0

c. what is the displacement at t=0

d .what will the displacement when it comes to rest

e .How much time it take to come to rest.

5. A man runs at a speed at 4 m/s to overtake a standing bus.When he is 6 m behind the door at t=0,the bus moves forward and continues with constant acceleration of 1.2 m/s

^{2}find the following

a. how long does it take for the man to gain the door

b if in the beginning he is 10m behind the door ,will he running at the same speed ever catch up bus?

**Detailed Solutions:**3. The time taken to reach the pole is given

R=v

_{0}cosθ tor t=R/v

_{0}cosθNow equation of motion of vertical motion

h=v

_{0}sinθt-1/2gt^{2}at t=R/v

_{0}cosθ h=Hso

H=(v

_{0}sinθ)X(R/v_{0}cosθ ) -(1/2)g( R/v_{0}cosθ)^{2}or H=Rtanθ-gR

^{2}/2v_{0}^{2}cos^{2}┴.

Given x=(-2/3)t

^{2}+16t+2Velocity=dx/dt=(-4/3)t+16

so velocity at t=0 =16

and velocity at t=1 =(-4/3)+16=44/3

Acceleration is given as =d

^{2}x/dt^{2}=-4/3so acceleration is time independent and it is constant

Displacement at t=0 can be found by simply substituting the values of t=0 in equation (1)

=2

Now v=(-4/3)t+16

when v=0

then t=4/3 sec

Displacement can be found by substituing the value of t=4/3 in equation (1)

=-32/27+64/3+2

=(-32+576+54)/27=598/27 m

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