Answer:
the maximum possible constant speed is 8 m/sec
Explanation:
from the image, Given that
r(t) = (2t, t²,t²/3), -5 ≤ t ≤ 5
Given that the curvature K(t) = 2 / ( t² + 2)²
note that t² + 2 ≥ 2
(t² + 2)² ≥ 4
1 / (t² + 2)² ≤ 1/4
2 / (t² + 2)² ≤ 1/2
Also note that k(0) = 1/2
The normal component of acceleration satisfies aN = kv²
where v = ║v(t)║is the speed of the roller coaster.
The maximum possible normal component of acceleration is 32
so, aN ≤ 32 every where on the track
aN = kv² ≤ 1/2v² ≤ 32
v² ≤ 64
Therefore, the maximum possible constant speed is 8 m/sec
The box is moving in the direction of Eduardo with a force of 300N since he is pulling 300N stronger than Clara.
Answer:
6840 N
Explanation:
The force acting on the car can be found by using Newton's second law:
F = ma
where
F is the net force on the car
m is the mass of the car
a is its acceleration
For the car in this problem,
m = 1800 kg
Substituting,
The magnitude of the resultant force is given by the centripetal force, since the car is under a circular motion. So, we have:
The centripetal acceleration is given by:
Where v is the linear speed and r the radius of the circular motion. Replacing this and solving:
Answer:
A. Speed is a scalar quantity and velocity is a vector quantity.
Explanation:
A scalar quantity is one that consists of only a numerical value.
Speed is a scalar quantity because only the instantaneous value is indicated, for example the speedometer of a car that tells you your speed at the moment but not where you are going or in what direction are you going.
On the other hand, velocity is a vector quantity. Because it is composed of a <u>magnitude and a direction</u>, for example 10m/s to the south is a velocity, and 10m/s is a speed.
