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1) In a circular track (distance 400 m) an athlete runs 1/4 the of the ground. So what would be the displacement ?

Ans: Given length of the circular track = 400m. Since the athlete runs ¼ of the circular track the distance covered by the athlete is 100m. The displacement is the shortest distance between the initial and final position, therefore, displacement in above question is length of the straight line AB as given in the diagram below.

To calculate length of the line AB we need to first calculate the radius of the circular track.

Now, Length of track = 2 ?R = 400

 400 =  2 ?R

              R  = 200 / ?

Now , In right triangle OAB; AB² = OA² + OB² 

                                                                      =   R² + R²

                                                     = ?(200/?)² + ?(200/?)²

                                                     ^{= 90.06 m}

2. A train travels 40 km at a uniform speed of 30 km/hr. Its average speed after travelling another 40 km is 45 km/hr for the whole journey. It’s speed in the second half of the journey is?

Ans: Suppose speed of the train in second half be v km/hr; Total distance travelled by the train = 80 km

Thus the speed to travel second half  = 90 km/hr

3.   A cheetah is fastest land animal and it can achieve a peak velocity of 100 km per hour up to distance less than 500 metres. If the cheetah spots his prey at a distance of 100 metres what is the minimum time it will take to get its prey?

                                                                                                                                          Ans: If the cheetah spots the prey at its top speed, the cheetah will hunt down the prey with the speed of 100 km/h. = 27.7 m/s Now, speed = d/t  time = d/s = 100/27.7 = 3.6 sec.

 So, the minimum time the cheetah will take to get the prey is 3.6 s.

4. 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

5..  A car moves with a speed of 30 km/h for half an hour; 25 km/h for 1 hr and 40 km/hr for 2 hrs. Find average speed.

Ans: Distance travelled with a speed of 30 km/h for half an hour= 30km/h × 1/2hr = 15 km

Distance travelled with a speed of 25 km/h for an hour = 25 km/h × 1hr  = 25km

Distance travelled with a speed of 40 km / h for 2 hour = 40 km/h × 2hr = 80km

6. If a travels first 40km at speed of 20 km/h and next 80 km at a speed of 40 km/h. What is the average speed of cat during journey?

7. On a 120 km long track, a train travels the first 30 km at a speed of 30 km/h. How fast train travel the next 90 km so that average speed would be 60 km/h?

Ans. Let train travel the next 90 km at speed x km/h, Average speed given = 60 km/h

8. An object covers half the distance with the speed of 20m/s and other half with a speed of 30m/s. Find average speed?

Ans: Let S be the total distance traveled by the object.

It covers (S/2) with speed 30 m/s. Time taken to cover this (S/2) 9s = (S/2) 30 = S/60

Average speed  = Total distance/total time  = (S/2 + S /2) / (S/40 + S/60)  = 24 m/s.

9. A car is travelling at 20 m/s along a road. A child runs out into the road 50 m ahead and the car driver steps on the brake pedal. What must the car’s deceleration be if the car is to stop just before it reaches the child?

Ans.

Acceleration = -4 m/s² or, retardation  = 4 m/s²