Ask a Teacher

Sir, please give me some questions related to velocity.

1.    A car travels a distance of 200 km from Delhi to Ambala towards North in 5 hours. Calculate; speed, velocity of the car for this journey.

Answer:

( I ) Speed = Distance travelled/Time taken

                   = 200 km/5h

                   = 40 km/h

Thus, the speed  ( or average speed)  of the are in 40 km/h.

(ii) Velocity = Displacement/Time taken

                     = 200 km towards North/5h

                     = 40 km/h towards North

So, the velocity ( or average velocity) of the car is 40 km/h towards North.

2.    A bus covers a distance of 250 km from the Delhi to Jaipur towards west in 5 hours in the morning and returns to Delhi in the evening covering the same distance of 250 km in the same time of 5 hours.  Find  1. Average Speed  and  2. Average Velocity of the bus for the whole journey.

Answer:

a.     Average speed = Total distance travelled/Total time taken

                         = 250 km + 250km/5h + 5h

                         =  500 km/10h

                         = 50 km/h.

Thus, the average speed of the bus for whole journey is 50 km/h.

b.    In this case, the bus travels 250 km from Delhi 10 Jaipur towards west and is then comes back to starting point Delhi in the reverse direction.  So, the total displacement will be 250km = 250 km = 0 km.

Now, Average velocity = Total displacement/Total time taken

                                       = 250 km - 250km/5h + 5h

                                       = 0 km/10 h = 0 km/h

Thus the average velocity of the bus for the whole journey is 0 km  per hour.

3.    A moving train is brought to rest within 20 records by applying track.  Find the initial velocity, of the retardation due to track in 2m/s²

Answer: 

       In this problem we have been given the value of retardation  but  require the value of  acceleration we known that retardation in negative acceleration.  So if the retardation is +2m/s², then the acceleration will be – 2m/s².

    Here, Initial velocity, u = ?

               Final velocity, v = 0

                 Acceleration, a = -2m/s²

                       And time, t = 20s.

We have   v = u + at
                  0 = u + ( -2 ) x 20
                  0 = u - 40

                  u = 40 m/s.

Initial velocity of train is 40 m/s.

4.    A wooden slab, starting from rest, slides down an inclined plane of length 10m with an acceleration of 5 m/s.  What would be its speed at the bottom of the inclined plane?

Answer:

We have s = ut + ½ at ²

              10 = ½ x 5 x  t²

                t = 2 s

                v = 0 + at

                   = 5 x 2

                   = 10 m/s

5.    Find the initial velocity of a train which is stopped by in 20s by applying  trakes.  The retardation due to trakes in 1.5 m/s²

Answer:

                  u = ?

t= 20s

v = 0

a = -1.5m/s²

v = u + at
0 = u – 1.5 x 20
   = u – 30
u = 30 m/s.

6.    An artificial satellite is moving in a circular  orbit of radios nearly 42,250km.  Calculate its linear velocity,  if it takes 24 hours to revolve around the earth.

Answer:

   Linear velocity, V = Distance travelled/Time taken

                                    =  2 ?rt

                                  = 2 x 22/7 x 42, 25/ 24 x 60 x 60

                                  = 3.07 km/s

7. A car is travelling along the road at 8m/s. It accelerates at 1m/s2 for a distance of 18m. How fast is travelling?

Ans: Applying; v² = u²  + 2 as

 v² = 64 + 2 x 8 

 v² = 100 So, v = 10m/s

8.     A police jeep is chasing velocity of 45 km/h. A thief in another jeep moving with a velocity of 153 km/h. police fires a bullet with muzzle velocity of 180 m/s the velocity it will strike the car of the thief is?

Ans: Given: Velocity of police jeep = 45 m/hr  = 12.5 m/s Velocity of thief’s jeep  = 153 km/hr = 42.5 m/s

Velocity of bullet  = 180 m/s

Now, since bullet is fired from police jeep which is going at 42.5 m/s,

Therefore, velocity of bullet is (180 + 12.5) = 192. 5 m/s.

To calculate velocity with which bullet with hit the thief we use concept of relative velocity.

Therefore, we have V_BT  = V_B - V_T Here VB is velocity of bullet and  VT is velocity of thief

V_BT = 192. 5m/s  -  42.5 m/s  = 150m/s