Question

A runner jogs 12 km North then turns and runs 5 km East in three hours. a) What is his displacement? b) Calculate his average speed. c) Calculate his average velocity (including the direction). On away an aircraft accelerates at m/ 2 for 15 s Its final velocity is 320​

Answer 1

Given:

The runner jogs 12 km North and then runs 5 km East.

The total time taken by the runner (T) = 3 hours

To Find:

(a) The displacement.

(b) The average speed of the runner.

(c) The average velocity of the runner.

Solution:

(a) The runner first jogs 12 km North and then turns and runs 5 km East.

∴ The total displacement of the runner = $\sqrt{12^{2} +5^{2} } =\sqrt{169}$ = 13 km

(b) The average speed of a journey is equal to the distance travelled per unit of time. It is equal to the total distance travelled (D) divided by the total time taken (T).

The total time taken by the runner (T) = 3 hours

∴ Total distance travelled (D) = 12 + 5 = 17 km

∴ The average speed of the runner = 17/3 km/hr

(c) The average velocity of a journey is equal to the displacement per unit of time. It is equal to the net displacement (d) divided by the total time taken (T).

The total time taken by the runner (T) = 3 hours

The total displacement of the runner = 13 km

∴ The average velocity of the runner = 13/3 km/hr

→ Let the angle that displacement makes with the north be 'θ'.

∴ tanθ = 5/12

∴ θ = tan⁻¹(5/12) = 22.62°

→ Therefore the average velocity as well as displacement both make an angle of 22.62° with the North direction towards to East.

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