Kinematics(Motion in a straight line with constant acceleration)(Problems)

1). A car travels the first half of a distance between two places at a speed of 30km/hr and second half of the distance at 50 km/hr. Find average speed of the car for the whole journey.

2). A motor car moving with a uniform speed of 20 m/s comes to a stop on the application of brakes after travelling a distance of 10 m. Find the acceleration of the car.

3). A body travels for 15 sec starting from rest with constant acceleration. If it travels distances S₁, S₂ and S₃ in the first 5 seconds, second 5 seconds and the third 5 seconds respectively, then find S₁:S₂:S₃.

4). The relation 3t=sqrt(3x) + 6 describes the displacement of a particle in one direction. Find the displacement of the particle when its velocity is zero.

5). A particle is moving eastwards with velocity of 5 m/s. In 10 sec, the velocity changes to 5 m/s northwards. Find the average acceleration.

Kinematics(Motion in a straight line with constant acceleration)(Problems)

1). The position of a particle along the x-axis is given by 9.75+1.5t³. Find:

(          a)    Average velocity between t=2 and t=3 seconds.

           b)   Instantaneous velocity at t=2 seconds.

           c)    Instantaneous velocity at t=2.5 seconds.

2). A motorcyclist moving with uniform retardation takes 10 sec and 20 sec respectively to travel
     successive quarter km. How much further will he travel before coming to rest?

3). A point moving in a straight line traversed half the distance with a velocity v₀. The remaining part of the
     distance was covered with velocity v₁ for half the time, and with velocity v₂ for the other half of the
     time. Find the mean velocity of the point averaged over the whole time of motion.
4).At the instant a traffic light turns green, a car starts with a constant acceleration of 2.2 m/s². At the same
    instant a truck, travelling with a constant speed of 9.5 m/s² overtakes and passes the car.
    (a) How far beyond the starting point will the car overtake the truck?

    (b) How fast will the car be travelling at the instant?

5).A train is crossing an observer standing on a platform. The first compartment of the train takes 2 sec to
    cross the observer while the second compartment of the train takes 2.5 sec to cross him. The train is
    moving with uniform acceleration. Find

    (a) Velocity of the train when the front of the first compartment crosses the observer.

    (b) The acceleration of the train

    (The length of each compartment is 15 m.)

Kinematics(Basic Definitions)(Numericals 6 to 9)

6).  A particle moves in a circle of radius R=21/22 m with constant speed 1 m/s. Find:
     (a) Magnitude of average velocity in 2 seconds
     (b) Magnitude of average acceleration in 2 seconds

7).  A particle is moving in x-y plane. At time t=0, particle is at (1,2) and has velocity 4i+6j. At t=4, particle reaches (6,4) and has velocity 2i+10j. In the given time interval, find,
     (a) Average velocity
     (b) Average Acceleration

8).  A particle is moving in a circle of radius 4 cm with constant speed of 1cm/s. Find:
     (a) Time period of the particle
     (b) Average speed of the particle in time t=0 to t=1 sec.
     (c) Average velocity of the particle in time t=0 to t=1 sec.
     (d) Average acceleration of the particle in time t=0 to t=1 sec.

9). A particle moves in a straight line with a constant speed of 4m/s for 2seconds, then with 6 m/s for 3 seconds. Find the average speed of the particle in the given time interval.

Kinematics(Basic Definitions)(Numericals 1 to 5)

1). A farmer has to go to 500 m due north, 400 m due east and 200 m due south to reach his field. If he takes 20 minutes to reach the field:
     (a)  Find distance
     (b)  Find displacement
     (c)  Find average speed
     (d)  Find average velocity

2). The length of a seconds hand in watch is 1 cm. Find the change in the velocity of its tip in 15 seconds.

3). A particle moving along a straight line travels half of a distance with uniform speed 30 m/s and the remaining half of the distance with speed 60 m/s. Find the average speed of the particle.

4). A car moves with 60 km/hr in the first 1 hour and with 80 km/hr in the next half and hour. Find:
     (a).  total distance travelled by the car.
     (b).  average speed of the car in total 1.5 hours

5). A block moves in a straight line with velocity v for time t. Then its velocity become 2v for next time interval t. Finally its velocity becomes 3v for time T. If average velocity during the complete journey was 2.5v, then find T in terms of t. 

Kinematics(Basic Definitions)(Theory Portion)

Theory Portion:
1).  Position Vector
2).  Displacement Vector
3).  Distance
4).  Average Velocity
5).  Average Speed
6).  Instantaneous Speed
7).  Instantaneous Velocity
8).  Average Acceleration
9).  Instantaneous Acceleration