# Numerical Problems on Displacement, Average Speed, Velocity

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#### Example – 1:

• A train travels a distance of 100 m due east. What is its speed and velocity?

Speed = distance /time = 100/10 = 10 m/s

velocity = 10m/s  due east

#### Example – 2:

• A train moving with a uniform speed covers a distance of 120 m in 2 s. Calculate the speed of the train and time taken to cover a distance of 240m.
• Solution:
• 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.

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 train is 60 m/s and it will take 4 s to cover a distance of 240 m

#### Example – 3:

• A car takes 3 hours to travel from Delhi to Agra with a uniform speed of 65 kmph. Find the distance between the cities.
• Solution:
• Given: Speed of car = v = 65 km/h, Time taken = t = 3 hours
• To Find: Distance = s = ?.

For uniform motion, Distance = speed x time = 65 x 3 = 195 km

Ans: The distance between delhi and Agra is 195 km

#### Example – 4:

• A body travels at a uniform speed of 20 m/s. Find the distance travelled by the body in 10 s.
• Solution:
• Given: Speed of body = v = 20 m/s, Time taken = t = 10 s
• To Find: Distance = s = ?.

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 – 5:

• A car is travelling with a uniform speed of 72 kmph. Find the distance travelled by it in 20 minutes
• Solution:
• 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 = ?.

For uniform motion, Distance = speed x time = 20 x 1200 = 24000 m = 24 km

Ans: The distance travelled by car is 24 km

#### Example – 6:

• 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.
• Solution:
• Given: Upward distance travelled = 100 m, time taken for upward journey = 5s

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 – 7:

• A car travels at a uniform speed of 30 kmph for 30 minutes and then at a uniform speed of 40 kmph for next 40 min. Calculate the total distance travelled by car and its average speed.
• Solution:
• 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 =?

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 – 8:

• 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.
• Solution:
• 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 =?

Total distance travelled = s = s1 + s2 = v1t1 + v2t2 = 30x (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 – 9:

• 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.
• Solution:
• 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 =?

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 = 48 kmph

Ans: The average speed = 48 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.
• Solution:
• 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 =?

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.
• Solution:
• Given:  Initial reading = s1 = 1272 km, Final reading = s2 = 1352 km, time taken = 50 min = 50/60 = 5/6 h
• To Find:  average speed =?

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?
• Solution:
• 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 =?

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 car has a reaction time of 0.2 s. reaction time is a time between actually seeing the obstacle and applying 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.
• Solution:
• 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 =?

Between the 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

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