1) The distance is 12 km
2) The speed is 4 km/h
3) The displacement is 8.6 km at [tex]35.5^{\circ}[/tex] north of west
4) The velocity is 2.87 km/h at [tex]35.5^{\circ}[/tex] north of west
Explanation:
1)
The distance covered by an object is the total length of the path covered by the object during its motion, regardless of its direction. Distance is a scalar quantity.
In this problem, the person walks:
5 km North
and then
7 km west
So, the distance covered is:
d = 5 km + 7 km = 12 km
And being a scalar, distance has no direction.
2)
Speed is a scalar quantity that tells "how fast" an object is moving. It is defined as:
[tex]speed=\frac{d}{t}[/tex]
where
d is the distance covered
t is the time taken
In this problem, we have
d = 12 km is the distance
t = 3 h is the time taken
Substituting,
[tex]speed = \frac{12 km}{3h}=4 km/h[/tex]
And being a scalar, speed has no direction.
3)
Displacement is a vector quantity; it is a vector connecting the initial position to the final position of motion. Therefore, its magnitude must be found by using the rules of vectors.
In this problem, the person walks:
5 km North
and then
7 km West
The two motions are at right angle, so they form the sides of a right triangle, of which the hypothenuse corresponds to the displacement. Therefore, we can find it by using Pythagorean's theorem:
[tex]d=\sqrt{7^2+5^2}=8.6 km[/tex]
Being a vector, displacement has also a direction, given by:
[tex]\theta=tan^{-1}(\frac{5}{7})=35.5^{\circ}[/tex] north of west.
4)
Velocity is a vector quantity, given by:
[tex]velocity = \frac{d}{t}[/tex]
where
d is the displacement
t is the time taken
In this problem, we have
d = 8.6 km (displacement)
t = 3 h (time taken)
Therefore, the velocity is
[tex]v=\frac{8.6 km}{3 h}=2.87 km/h[/tex]
And being a vector, velocity has also a direction, which is the same of the displacement: so, [tex]35.5^{\circ}[/tex] north of west.
Learn more about distance and displacement:
brainly.com/question/3969582
About speed and velocity:
brainly.com/question/8893949 (speed)
brainly.com/question/5063905 (speed vs velocity)
brainly.com/question/5248528 (velocity)
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