man travels 75 m [N] and 62 m [E] in a time of 148 s. Determine his speed and velocity.
d = sqrt (75^2 + 62^2)
speed = (d /148) meters/second
East (x) component = speed * 62/d
North (y) component = speed * 75/d
To determine the speed and velocity of the man, we first need to find the total distance traveled and the displacement.
The total distance traveled is the sum of the distances traveled in each direction:
Distance North (dN) = 75 m
Distance East (dE) = 62 m
Total distance (d) = dN + dE
= 75 m + 62 m
= 137 m
The displacement is the straight-line distance and direction from the starting point to the endpoint. We can use Pythagoras' theorem to find the displacement (dDisplacement):
dDisplacement = √(dN² + dE²)
= √(75 m)² + (62 m)²
= √(5625 m² + 3844 m²)
= √(9469 m²)
≈ 97.3 m
Now, we can calculate the speed by dividing the total distance (d) with the time taken (t):
Speed = d / t
= 137 m / 148 s
≈ 0.93 m/s
Finally, we can determine the velocity by dividing the displacement (dDisplacement) with the time taken (t), considering the direction:
Velocity = dDisplacement / t = 97.3 m / 148 s
The direction of the displacement should also be mentioned, but it is not given in the question.
To determine the man's speed and velocity, we first need to understand the difference between speed and velocity.
Speed is a scalar quantity that indicates how fast an object is moving. It is calculated by dividing the total distance traveled by the total time taken.
Velocity, on the other hand, is a vector quantity that not only indicates the speed of an object but also its direction. It is calculated by dividing the displacement (change in position) of an object by the total time taken.
In this case, the man travels 75 m north and 62 m east. To calculate his speed, we need to find the total distance traveled, which can be found using the Pythagorean theorem.
Using the Pythagorean theorem, we can calculate the total distance traveled (d) as follows:
d = √(75^2 + 62^2)
d ≈ 97.49 m (rounded to two decimal places)
Now, to calculate the speed, we divide the total distance traveled by the total time taken:
Speed = Total Distance / Total Time
Speed = 97.49 m / 148 s
Speed ≈ 0.66 m/s (rounded to two decimal places)
To calculate velocity, we need to find the displacement. Displacement is a vector that represents the change in position from the starting point to the ending point.
In this case, the displacement can be calculated as follows:
Displacement = √((75^2 - 62^2)^2 + (75 * 62)^2)
Displacement ≈ 96.42 m (rounded to two decimal places)
Now, we can calculate the velocity by dividing the displacement by the total time taken:
Velocity = Displacement / Total Time
Velocity = 96.42 m / 148 s
Velocity ≈ 0.65 m/s (rounded to two decimal places)
Therefore, the man's speed is approximately 0.66 m/s, and his velocity is approximately 0.65 m/s.