Motion Test

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Motion Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

Two trains with lengths 180 m and 220 m respectively, are running in opposite directions with speeds of 40 km/hr and 50 km/hr respectively. The time taken by them in crossing each other will be

A
16 sec

B
17 sec

C
18 sec

D
22 sec

Solution

u = 40 km/hr
v = 50 km/hr
l = 180 m

L = 220 m
Now, we know that speed = distance/time
u+v = l+L / time (When trains move in opposite directions, their speeds are added.)

u+v = 40+50 = 90 km/hr = 90*5/18 = 25 m/s
l+L = 180+220 = 400 m

25 = 400/t
Hence, t = 16 sec
Question 2
1 / -0

The wheel of an engine, with a circumference of 25 decimetres, makes 10 revolutions in 4 seconds. The speed of the wheel (in km/hr) is

A
16

B
22.5

C
32.8

D
36

Solution

Circumference of wheel = 25 dm = 2.5 m
The wheel makes 10 revolutions in 4 s.

Then, in one second = 10/4 = 2.5 revolutions
Speed of wheel = 2.5 x 2.5 = 6.25 m/s
Speed of wheel = 6.25 x 3600/1000 = 22.5 km/hr
Question 3
1 / -0

Two trains running in the same direction at 40 km/hr and 22 km/hr completely pass one another in one minute. If the length of the first train is 125 m, the length of the second train is

A
125 m

B
150 m

C
175 m

D
200 m

Solution

u = 40 km/hr
v = 22 km/hr
l = 125 m
t = 1 min = 60 sec
L = ?

Now, we know that speed = distance/time
u-v = l + L / time (When trains move in same direction, their speeds are subtracted.)
u-v = 40-22 = 18 km/hr = 18*1000/3600 = 5 m/s

5 = 125+L/60
Hence, L = 175 m
Question 4
1 / -0

If a body takes as much time to cover 10 m as a car takes to cover 25 m, the distance the body will cover during the time the car covers 1 km is

A
40 m

B
400 m

C
250 m

D
none of these

Solution

For 25 m of car, body covers = 10 m
For 1 m of car, body covers = 10/25 m
For 1000 m of car, body covers = 10/25 * 1000
= 400 m
Question 5
1 / -0

A train travels the first 15 km at a uniform speed of 30 km/hr, the next 75 km at a uniform speed of 50 km/hr and the last 10 km at a uniform speed of 20 km/hr. Calculate the average speed for the entire journey.

A
100 km/hr

B
40 km/hr

C
75 km/hr

D
20 km/hr

Solution

Time for first 15 km = 15/30 = 0.5 hr
Time for next 75 km = 75/50 = 1.5 hr
Time for next 10 km = 10/20 = 0.5 hr
Total time taken = 2.5 hr
Total distance = 15+75+10 = 100 km

Now, average speed = Total distance travelled / Total time taken
= 100/2.5 = 40 km/hr
Question 6
1 / -0

Gaurav travelled 1200 km by air which formed 2/5th of his trip. He travelled one-third of the remaining distance by car and the rest by train. The distance travelled by him in train was

A
480 km

B
800 km

C
1200 km

D
1800 km

Solution

2/5^th of the total distance covered by air = 1200 km
Hence, total distance covered by air = 1200*5/2 = 3000 km

1/3^rd of remaining distance covered by car = 1/3*1800 = 600 km
Distance covered by train = 1800-600 = 1200 km
Question 7
1 / -0

A train overtakes two persons who are walking at the rate of 2 km/hr and 4 km/hr in the same direction in which the train is going, and passes them completely in 9 and 10 seconds respectively. The length of the train (in meters) is

A
54

B
45

C
50

D
72

Solution

To find: Length of train (L)
Speed of train (s) = ?

Train passed first person (at 2 km/hr or 5/9 m/s) in 9 secs.
Train passed second person (at 4 km/hr or 10/9 m/s) in 10 secs.

For 1^st person,
s-5/9 = L/9 (When trains move in the same direction, their speeds are subtracted.)

or, 9s - L = 5 --------(i)

For 2^nd person,
s-10/9 = L/10
Or 90s - 9L = 100 ---------(ii)

Solving (i) and (ii), we get
Length of train = 50 m
Question 8
1 / -0

The distance between two points A and B is 110 km. A motorcyclist starts from A towards B at 7 a.m. at a speed of 20 km/hr. Another motorcyclist starts from B towards A at 8 a.m. at a speed of 25 km/hr. When will they cross each other?

A
9 am

B
11 am

C
10 am

D
12 am

Solution

Speed of 1^st motorcyclist = 20 km/hr
In 3 hrs or at 10 am, distance covered = 60 km

Speed of 2^nd motorcyclist = 25 km/hr
In 2 hrs or at 10 am, distance covered = 50 km

Total distance covered by both till 10 am = 60 + 50 = 110 km
Hence, they will cross each other at 10 am.
Question 9
1 / -0

Two trains starting at the same time from two stations, 200 km apart; and going in opposite directions cross each other at a distance of 110 km from one of stations. The ratio of their speeds may be

A
11:20

B
9:20

C
11:9

D
11:10

Solution

Let the distance covered by 1^st train = 110 km
Distance covered by 2^nd train = 90 km
Let the time taken by both = t hrs

Speed of 1^st train : Speed of 2^nd train
110/t : 90/t
11 : 9

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Re-Attempt Weekly Quiz Competition

Motion Test - 1

Result

Motion Test - 1

Score

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Rank

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SHARING IS CARING

Question 1

16 sec

17 sec

18 sec

22 sec

Solution

Question 2

16

22.5

32.8

36

Solution

Question 3

125 m

150 m

175 m

200 m

Solution

Question 4

40 m

400 m

250 m

none of these

Solution

Question 5

100 km/hr

40 km/hr

75 km/hr

20 km/hr

Solution

Question 6

480 km

800 km

1200 km

1800 km

Solution

Question 7

54

45

50

72

Solution

Question 8

9 am

11 am

10 am

12 am

Solution

Question 9

11:20

9:20

11:9

11:10

Solution

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