Science > Physics > Motion in a Straight Line > Numerical Problems on Displacement, Average Speed, Velocity
In this article, we shall study to solve problems to calculate displacement, Average Speed, and average Velocity.
Example – 01:
A train travels a distance of 100 m due east in 10 seconds. What is its speed and velocity?
Solution:
Speed = distance /time = 100/10 = 10 m/s
velocity = 10m/s due east
Ans: The speed is 10 m/s and the velocity is 10m/s due east
Example – 02:
A train moving with a uniform speed covers a distance of 120 m in 2 s. Calculate the speed of the train and the time taken to cover a distance of 240m.
Given: Distance travelled by train = s = 120 m, Time taken = 2 s
To Find: Speed of train = v =? and time t =? when s = 240 m.
Solution:
For uniform motion, speed = distance/time = 120/2 = 60 m/s
Time taken to cover 240 m, time = distance/speed = 240/60 = 4 s
Ans: The speed of the train is 60 m/s and it will take 4 s to cover a distance of 240 m
Example – 03:
A car takes 3 hours to travel from Delhi to Agra with a uniform speed of 65 kmph. Find the distance between the cities.
Given: Speed of car = v = 65 km/h, Time taken = t = 3 hours
To Find: Distance = s = ?.
Solution:
For uniform motion, Distance = speed x time = 65 x 3 = 195 km
Ans: The distance between delhi and Agra is 195 km
Example – 04:
A body travels at a uniform speed of 20 m/s. Find the distance travelled by the body in 10 s.
Given: Speed of body = v = 20 m/s, Time taken = t = 10 s
To Find: Distance = s = ?.
Solution:
For uniform motion, Distance = speed x time = 20 x 10 = 200 m
Ans: The distance travelled by the body in 10 s is 200 m
Example – 05:
A car is travelling with a uniform speed of 72 kmph. Find the distance travelled by it in 20 minutes
Given: Speed of car = v = 72 km/h = 72x 5/18 = 20 m/s, Time = t = 20 min = 20 x 60 = 1200 s
To Find: Distance = s = ?.
Solution:
For uniform motion, Distance = speed x time = 20 x 1200 = 24000 m = 24 km
Ans: The distance travelled by car is 24 km
Example – 06:
A body rises vertically upward to a height of 100 m, in 5 seconds, then comes back at the same position after another 5 s. Find the distance travelled, displacement, average speed and average velocity of the body.
Given: Upward distance travelled = 100 m, time taken for upward journey = 5s
Solution:
Total distance travelled = distance travelled in upward journey + distance travelled in downward journey
Total distance travelled = 100 m + 100 m = 200 m
As the body is returning back to the same position.
Displacement = minimum distance between initial and final position = 0
Average speed = Total distance/ total time = 200/10 = 20 m/s
As displacement is zero, velocity is also zero
Example – 07:
A car travels at a uniform speed of 30 kmph for 30 minutes and then at a uniform speed of 40 kmph for the next 40 min. Calculate the total distance travelled by car and its average speed.
Given: Speed for the first part of journey = v1 = 30 kmph, time for first part of journey = t1 = 30 min = 30/60 = 1/2 h, Speed for the second part of journey = v2 = 40 kmph, time for first part of journey = t2 = 40 min = 40/60 = 2/3 h,
To Find: Total distance travelled =? and average speed =?
Solution:
Total distance travelled = s = s1 + s2 = v1t1 + v2t2 = 30x (1/2) + 40 x (2/3)
Total distance travelled = 125/3 = 41.67 km
Total time taken = t = t1 + t2 = 1/2 + 2/3 = 7/6 h
Average speed = Total disrtance travelled / Total time taken
Average speed = (125/3)/(7/6) = 35.71 kmph
Ans: Total distance travelled = 41,67 km and average speed = 35.71 kmph
Example – 08:
A car travels at a uniform speed of 30 kmph for 30 minutes and then at a uniform speed of 60 kmph for next 30 min. Calculate the average speed of the car.
Given: Speed for the first part of journey = v1 = 30 kmph, time for first part of journey = t1 = 30 min = 30/60 = 1/2 h, Speed for the second part of journey = v2 = 60 kmph, time for first part of journey = t2 = 30 min = 30/60 = 1/2 h,
To Find: Total distance travelled =? and average speed =?
Solution:
Total distance travelled = s = s1 + s2
Total distance travelled = v1t1 + v2t2
Total distance travelled = 30 x (1/2) + 60 x (1/2)
Total distance travelled = 15 + 30 = 45 km
Total time taken = t = t1 + t2 = 1/2 + 1/2 = 1 h
Average speed = Total disrtance travelled / Total time taken
Average speed = 45/1 = 45 kmph
Ans: The average speed = 45 kmph
Example – 09:
A car travels first 30 km at a uniform speed of 30 kmph and next 30 km at a uniform speed of 60 kmph. Calculate the average speed of the car.
Given: Distance travelled in first part of journey = s1 = 30km, Speed for the first part of journey = v1 = 30 kmph, Distance travelled in second part of journey = s2 = 30km, Speed for the second part of journey = v2 = 60 kmph,
To Find: average speed =?
Solution:
Total distance travelled = s = s1 + s2 = 30 km + 30 km = 60 km
Total time taken = t = t1 + t2 = s1/v1 + s2/v2 = 30/30 + 30/60 = 1.5 h
Average speed = Total disrtance travelled / Total time taken
Average speed = 60/1.5 = 40 kmph
Ans: The average speed = 40 kmph
Example – 10:
A car travels first 50 km at a uniform speed of 25 kmph and next 60 km at a uniform speed of 20 kmph. Calculate the average speed of the car.
Given: Distance travelled in first part of journey = s1 = 50km, Speed for the first part of journey = v1 = 25 kmph, Distance travelled in second part of journey = s2 = 60km, Speed for the second part of journey = v2 = 20 kmph,
To Find: average speed =?
Solution:
Total distance travelled = s = s1 + s2 =50 km + 60 km = 110 km
Total time taken = t = t1 + t2 = s1/v1 + s2/v2 = 50/25 + 60/20 = 5 h
Average speed = Total disrtance travelled / Total time taken
Average speed = 110/5 = 22 kmph
Ans: The average speed = 22 kmph
Example – 11:
A car is fitted with a speedometer which also gives reading of distance travelled by the car. At the start of the trio reading was found to be 1272 km and after 50 imutes at end of the trip is 1352 km. Calculate the average speed of the car.
Given: Initial reading = s1 = 1272 km, Final reading = s2 = 1352 km, time taken = 50 min = 50/60 = 5/6 h
To Find: average speed =?
Solution:
Total distance travelled = s2 – s1 = 1352 – 1272 = 80 km
Average speed = Total disrtance travelled / Total time taken
Average speed = 80/( 5/6)= 96 kmph
Ans: The average speed = 96 kmph
Example – 12:
A train takes 2 h to reach from station A to station B which is at a distance of 200 km from station A. It takes 3 h for the return journey. What is the average speed and average velocityof the train?
Given: Distance travelled in first part of journey = s1 = 200 km, time taken for the first part of journey = t1 = 2 h, Distance travelled in second part of journey = s2 = 200 km, time taken for the second part of journey = t2 = 3 h.
To Find: average speed =?
Solution:
Total distance travelled = s = s1 + s2 = 200 km + 200 km = 400 km
Total time taken = t = t1 + t2 = 2 h + 3 h = 5h
Average speed = Total disrtance travelled / Total time taken
Average speed = 400/5 = 80 kmph
As the train is coming back to starting point its displacement is zero.
Hence its average velocity = 0
Ans: The average speed = 80 kmph, average velocity = 0
Example – 13:
A driver of a car has a reaction time of 0.2 s. reaction time is a time between actually seeing the obstacle and applying the brake. He is moving with a uniform speed of 30 kmph. He spots a boy crossing the road. How much distance he travels before applying the brake.
Given: Reaction time = t = 0.2 s, speed of car = v = 36 kmph = 36 x 5/18 = 10 m/s
To Find: distance travelled = s =?
Solution:
Between seeing the boy and applying the brake car moves in uniform motion
Distance travelled before applying brake = s = v t = 10 x 0.2 = 2 m
Ans: Distance travelled before application of brakes is 2 m
Previous Topic: The Concept and Terminology of Motion
Next Topic: Newton’s Kinematical Equations of Motion
14 replies on “Numerical Problems on Displacement, Average Speed, Velocity”
Nice wedsit
Bro 9th question ka answer 40 hona chahiya mere hisaab se
Thank you Shivansh for correction
Very helpful…..but you have to increase the level of the questions…..
We are working on it. We are going to add questions where application of knowledge is important.
In the first Question time isn’t mentioned so How did you calculated time? Tell reply Early 🙏🙏
By the Way Amazing Website. The Question level & attractive interface are Just Amazing!
The problem was incomplete. Problem statement corrected. Thank you for bringing out the error.
Very nice website it helped me a lot Thanks
Did not understand the 8th question solution.[not the 7th question]
Can you help with it.
I have reformatted the problem. Just check it again and still, you have a problem? just comment.
nice problems keep it up
Nice problems but many problems are of same type only the value was changed and other questions are similar to each other please try to add different varieties of questions..
Nice questions.
🙏 Thank you 🙏
Average speed problems 🥺🥺🥺🥺🥺