# Practice – Solve problems involving distance and displacement

Questions :

You are running in a straight line. You ran 3km to the right and then you ran back for 1km. How much distance you have covered and what is your displacement from the starting point. ( Take “right” side as positive)

A hiker hiked 8km towards the North and then he hiked 6km towards the West. Draw a diagram to present the scenario. Find the distance covered and displacement of the hiker from the starting point. ( Take “East” and “North” as positive direction)

A car drives 5km towards the north, then 3km towards the east, and then 4km towards the south. Draw a diagram to present the scenario.

a) Find the distance covered by the car

b) Find the displacement of the car.

c) Can you plot the x-t graph from the information given?

You are walking in a straight line. You walked 5km towards the right and then you turned and walked back 2km. You took 1hour to cover every km.

a) How much distance have you covered?

c) Plot the x-t graph for this motion.

d) Do your answers from (a) and (b) agree with the graph?

You are walking in a straight line. You take 3 steps forward towards the right and then 2 steps back towards the left.  Each step is 1m long and requires 1s. If the right side is positive and if you repeat this motion 2 times,

a) Plot the x-t graph to show your motion.

b) Find the distance covered.

c) Find the displacement.

You are walking in a straight line. You take 3 steps forward towards the right and then 2 steps backward. Each forward step is 1m long and each backward step is 2m long. Each step requires 1s. If the right side is positive and if you repeat this motion 2 times,

a) Plot the x-t graph to show your motion.

b) Find the distance covered.

c) Find the displacement.

The x-t plot for a car is shown below. Study the plot carefully and answer the questions.

a) Describe the motion in the interval t2 – t3 and t6-t7.

b) Describe the motion at t4.

c) Describe the motion at t7.

d) What is the displacement?

Explanations :

You are running in a straight line. You ran 3km to the right and then you ran back for 1km. How much distance you have covered and what is your displacement from the starting point. ( Take “right” side as positive)

Distance covered = 3 km + 1 km = 4 km

Displacement = 3 km – 1km = 2 km to the right

A hiker hiked 8km towards the North and then he hiked 6km towards the West. Draw a diagram to present the scenario. Find the distance covered and displacement of the hiker from the starting point. ( Take “East” and “North” as positive direction)

Total Distance covered = 8 km + 6 km = 14 km

Displacement = √(8² + 6² ) = √(100) = 10 km towards North West

A car drives 5km towards the north, then 3km towards the east, and then 4km towards the south. Draw a diagram to present the scenario.

a) Find the distance covered by the car.

b) Find the displacement of the car.

c) Can you plot the x-t graph from the information given?

a) Distance Covered = 5 + 3 + 4 = 12 km

b) Displacement = √(3² + 1² ) = √10 km towards North-East

c) We cannot plot the x-t graph as time information is not given.

You are walking in a straight line. You walked 5km towards the right and then you turned and walked back 2km. You took 1hour to cover every km.

a) How much distance have you covered?

5 km + 2 km = 7 km

5 km – 2 km = 3 km towards right

c) Plot the x-t graph for this motion.

d) Do your answers from (a) and (b) agree with the graph?

You are walking in a straight line. You take 3 steps forward towards the right and then 2 steps back towards the left.  Each step is 1m long and requires 1s. If the right side is positive and if you repeat this motion 2 times,

a) Plot the x-t graph to show your motion.

b) Find the distance covered.

3m + 2m + 3m + 2m = 10m

c) Find the displacement.

Displacement = final position – initial position = 2 – 0 = 2m towards right

You are walking in a straight line. You take 3 steps forward towards the right and then 2 steps backward. Each forward step is 1m long and each backward step is 2m long. Each step requires 1s. If the right side is positive and if you repeat this motion 2 times,

a) Plot the x-t graph to show your motion.

b) Find the distance covered.

3m + 4m + 3m + 4m = 14m

c) Find the displacement.

Displacement = Finale position – Start position = – 2 – 0 = -2 m towards left

The x-t plot for a car is shown below. Study the plot carefully and answer the questions.

a) Describe the motion in the interval t2 – t3 and t6-t7.

The car is at rest in these intervals.

b) Describe the motion at t4.

The car starts moving in the opposite direction at t4.

c) Describe the motion at t7.

The car starts moving in the opposite direction at t7.

d) What is the displacement?

The displacement is 0.

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