1. A boy walks 4 m north and then turns to his right and walks 3 m more. Calculate his distance and displacement. If he takes 5s(sec) to walk this distance, find his speed as well as velocity for this journey.
Answers
Solution:
A boy walks 4 m north and then turns to his right and walks 3 m more. [See diagram]
Distance is the path covered by an object from its initial position to final position.
Distance = 4 m + 3 m = 7 m
Displacement is the shortest path from its initial position to final position.
And as we see diagram the path x is the shortest path. This makes it a right angle triangle . To calculate x we will apply Pythagoras Theorem and also Displacement will be x
Displacement =>
By Pythagoras Theorem ,
Perpendicular² + Base² = Hypotenuse²
4² + 3² = x²
16 + 9 = x²
√25 = x
x = 5
Displacement will be 5 m.
Speed tells us how fast an object is moving or it is the distance traveled per unit time.
To find speed ,
Speed = Distance / Time
Speed = 7 / 5
Speed = 1.4 m/s
Velocity tells us the speed of object in a particular direction.
To find velocity,
Velocity = Displacement / Time
Velocity = 5 / 5
Velocity = 1 m/s
The distance traveled by the boy is 7 m and the displacement of the boy is 5 m.
The speed and velocity of the boy is 1.4 m/s and 1 m/s respectively.
Explanation:
The distance traveled by the boy is:
d = 4 m + 3 m = 7 m
The starting point to ending point of the boy forms a right angled triangle.
The displacement of the boy is:
D = √(4² + 3³) = √(16 + 9) = √(25)
∴ D = 5 m
The speed is given by the formula:
Speed = Distance/time
The speed of the boy is:
∴ s = 7/5 = 1.4 m/s
The velocity is given by the formula:
Velocity = Displacement/time
The velocity of the boy is:
∴ v = 5/5 = 1 m/s