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Solved Examples 
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Ques 1: A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?
Ans: Distance covered in one round = 40 m
Time taken = 40s
Total time of journey = 2 min. 20s = 140 s
Total distance covered = = 140 m
Total rounds = = 3.5 round
After every complete round, the farmer will be at the starting point, hence after 3.5 rounds farmer will be at the diagonal ends of the field.
Displacement = 10√2m
Ques 2: In a longdistance race the athletes were expected to take four rounds of the track such that the line of finish was the same as the line of start. Suppose the length of the track was 200 m
(i) What is the total distance to be covered by the athletes?
(ii) What is the displacement of the athletes when they touch the finish line?
(iii) Is the motion of the athlete's uniform or nonuniform.
(iv) Is the displacement of an athlete and the distance moved by him at the end of the race equal?
Ans: (i) Total distance covered = 4 × 200m = 800 m
(ii) As the athletes finish at the starting line
Displacement = final positioninitial positive = r_{A}r_{A} = 0
(iii) Motion is nonuniform as the direction of motion of the athlete is changing while running on the track.
(iv) Displacement and distance moved are noted as Casual.
Ques 3: On a 120 km track, a train travels the first 30 km with a uniform speed of 30 km/h. How fast must the train travel the next 90 km so as to average 60 km/h for the entire trip?
Ans: Total distance d = 120 km
Average speed V_{av} = 60 km/h
Total time = t = ?
Average speed = Total distance/Total time taken
V_{av} = d/t
t = Putting the values
t = 120km/60km/h = 2h .............(i)
Distance travelled in first part of trip
d_{1} = 30 km
Speed in first part of the trip v_{1} = 30 km/h
Time taken in first part of trip
t_{1} = ?
t_{1} = putting the values
t_{1} = 30km/30km/h = 1 h
Time taken left to complete second part of the trip
t_{2} = t  t_{1} = 2  1 = 1h
Distance to be covered in second part of the trip
d_{2} = 90 km
reQues uired speed in second part
v_{2} = ?
speed = distance/time
v_{2} = d_{2}/t_{2} = 90 km/h
Ques 4: Nisha swims in a 90 m long pool. She covers 180m in one minute by swimming from one end to the other and back along the same straight path. Find the average speed and average velocity of Nisha.
Ans:
Total distance = 180 m
Total displacement = 0
Time taken t = 1min. = 60 s
Average speed (V_{av}) = Total distance/Total time taken
V_{av} = 180/60 = 3 m/s
Average velocity
(V_{av}) = Total distance/Total time taken
V_{av} = 0/60 = 0 m/s
Ques 5: A bus decreases its speed from 80 km/h to 60 km/h is 5 seconds. Find the acceleration of the bus.
Ans: u = 80 km/h = 80 × = 22.22 m/s
v = 60 km/h = 60 × = 16.67 m/s
time t = 5s
Acceleration (a) = (V  U) / t
a = (16.6  22.2)/5 = _ 1.11 m/s^{2}
Ques 6: A train starting from a railway station and moving with uniform acceleration, attains a speed 40 km/h in 10 minutes. Find its acceleration.
Ans: u = 0 (starting from rest)
v = 40 km/h = 40 × = 11.11 m/s
time t = 10 minutes = 600s
Acceleration
Ques 7: A bus between Kota to Jaipur passed the 100 km, 160 km and 220 km points at 10.30 am, 11.30 am and 1.30 pm. Find the average speed of the bus during each of the following intervals :
(a) 10.30 am to 11.30 am,
(b) 11.30 am to 1.30 pm and
(c) 10.30 am to 1.30 pm.
Ans:
(a) The distance covered between 10.30 am and 11.30 am is 160 km _ 100 km = 60 km. The time interval is 1 hour. The average speed during this interval is _ v_{1} = 60km/1h = 60 km/h.
(b) The distance covered between 11.30 am and 1.30 pm is 220 km _ 160 = 60 km. The time interval is 2 hours.
The average speed during this interval is v_{2} = 60km/2h = 30 km/h
(c) The distance covered between 10.30 am and 1.30 pm is 220 km, 100 km = 120 km. The time interval is 3 hours.
The average speed during this interval is, v_{3} = 120km/3h = 40 km/h.
Ques 8: The average speed of a bicycle, an athlete and car are 18 km/h, 7 m/s and 2 km/min. respectively. Which of the three is the fastest and which is the slowest?
Ans: 18 km/h = 18km/1h = 18000m/3600s = 5 m/s
2 km/min = 2km/1min = 2000m/60s = 33.3 m/s
Thus the average speeds of the bicycle, the athlete and the car are 5 m/s, 7 m/s and 33.3 m/s respectively. So the car is the fastest and the bicycle is the slowest.
Ques 9: An object is sliding down on the inclined plane. The velocity changes at a constant rate from 10 cm/s to 15 cm/s in 2 seconds. What is its acceleration?
Ans:
The situation is shown in figure. Let us take BA as the positive direction. The velocity at t = 0 is u = 10 cm/s and that at t = 25 is v = 15 cm/s.
Thus, a =
Ques 10: Figure shows the distancetime graph of two objects A and B which object is moving with greater speed when both are moving?
Ans: The line for object B makes a longer angle with the timeaxis. Its slope is longer than the slope of the line for object A. Thus, the speed of B is greater than that of A.
Ques 11: Figure represents the speedtime graph for a particle. Find the distance covered by the particle between t = 10 min. and t = 30 min.
Ans: We draw perpendicular lines from the 10minute point and the 30minute point to the timeaxis (fig.) The distance covered is equal to the area of the rectangle ABCD its value is ABCD = (30  10) × (10) = 20 × 10 = (20/60) × 10 = 10/3 km.
Ques 12: Find the distance covered by a particle during the time interval t = 0 to t = 20 s for which the speedtime graph is shown in figure.
Ans: The distance covered in the time interval 0 to 20 s.
Area of the shaded triangle = 1/2 × base × height. = 1/2 × (20) × (20) = 200 m.
Ques 13: Figure shows the velocitytime graphs for two objects, A and B, moving along the same direction. Which object has greater acceleration?
Ans: The slope of the velocitytime graph of B is greater than that for A, Thus, the acceleration of B is greater than that of A.
Ques 14: A particle moves through a distance of 3 m due east and then 4m due north.
(a) How much is the net distance traversed?
(b) What is the magnitude of the net displacement?
Ans: The situation is shown in the figure. The particle starts from O. It moves through a distance of 3m due east to reach A and then through a distance of 4m due north to reach B.
(a) The total distance moved is 3m 4m = 7 m,
(b) The magnitude of the net displacement is OB. In the right_angled triangle OAB,
OB^{2} = OA^{2} + AB^{2} = (3m)^{2} + (4m)^{2} = 9m^{2} + 16m^{2} = 25m^{2} OR OB = 5 m,
Ques 15: A car moves 30 km. in 30 min. and the next 30 km. in 40 min. calculate the average speed for the entire journey.
Ans: Given, the total time taken is 30 min + 40 min. = 70 min.
the total distance traversed = 30km + 30 km = 60 km.
The average speed v_{av} = 60km/70min  60km/(70/60)h  3600/70 km/hr = 51.4 km/h
Ques 16: A boy runs for 10 min. at a uniform speed of 9 km/h. At what speed should he run for the next 20 min. So that the average speed comes to 12 km/h?
Ans: Total time = 10 min 20 min = 30 min.
The average speed is 12 km/h. using s = vt,
the distance covered in 30 min = 12 km/h × 30 min = 12km/h x 1/2h = 6km
The distance covered in the first 10 min = 9 km/h × 10 min. = 9km/h x 1/6h = 1.5 km
Thus, he has to cover 6 km  1.5 km = 4.5 km. in the next 20 min.
The speed required is 4.5km/20min = 4.5km/(20/60)h = 13.5 km/h
Ques 17: A particle was at rest from 9:00 am to 9:30 am. It moved at a uniform speed of 10 km/h from 9:30 am to 10:00 am. Find the average speed between
(a) 9:00 am and 10:00 am
(b) 9:15 am and 10:00 am
Ans:(a) The distance moved by the particle between 9:30 am and 10:00 am is
s = vt = 10km/h x 1/2h = 5 km.
This is also the distance moved between 9:00 am and 10:00 am. Thus, the average speed during this interval is
v_{av} = s/t = 5km/1h = 5 km/h
(b) The distance moved between 9:30 am and 10:00 am is 5km. This is also the distance moved in the interval 9:15 am to 10:00 am. The average speed during this interval is _
v_{av} = s/t = 5km / 45min = 6.67 km/h.
Ques 18: It is estimated that the radio signal takes 1.27 seconds to reach the earth from the surface of the moon. Calculate the distance of the moon from the earth. Speed of radio signal = 3 × 10^{8} ms^{1} (speed of light in air).
Ans: Here, time = 1.27 s
speed = 3 × 10^{8} ms^{1}
distance = ?
Using distance = speed × time, we get
distance = 3 × 10^{8} × 1.27 = 3.81 × 10^{8} km = 3.81 × 10^{5} km
Ques 19: A wireless signal is sent to earth from a spacecraft. This signal reaches the earth in 300 seconds. Calculate the distance of the spacecraft from the earth. Given, speed of the signal = 3 × 10^{8} ms^{1}.
Ans: Here, t = 300 s
Speed, v = 3 × 10^{8} ms^{1}
Distance = ?
Using distance = speed × time, we get
distance = 3 × 10^{8} × 300 = 9 × 10^{10} m = 9 = 10^{7} km
Thus, distance of spacecraft from earth = 9 × 10^{7} km.
Ques 20: A sound is heard 5 seconds later than the lightning is seen in the sky on a rainy day. Find the distance of the location of lightning. Given speed of sound = 346 ms^{1}.
Ans: Here, t = 5 s
Speed, v = 346 ms^{1}
Distance = ?
Using distance = speed × time, we get
distance = 346 ms^{1} × 5 s = 1730 m
Thus, distance of the location of lightning = 1730 m
 Go through detailed chapter notes of this chapter here.
 You can find NCERT Solution of the chapter here.
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