The definition of velocity is a speed in a given direction. So the unit must include the speed and the direction that the object is moving. C. 31 m/s north is the correct answer, because the unit has the speed and the distance included. Although D has the same factors in it's answer, speed is only distance divided by time, and is not squared as it is shown incorrectly in answer D.
Conservation of energy means that initial kinetic energy =maximum gravitational potential energy. 1/2 * 3 * 10^2 = 150J. The gravitational potential energy at the top is 150 joules. The gravitational potential energy is calculated through mgh, so 150 = 3 * 10 * h. Height is 5 meters
Answer:
a) 45 s , b) vₐ = 90 m / s, v_b = 162 m / s, c) x_b = 3.328 10⁴ m
Explanation:
We can solve this exercise using the kinematic relations
Vehicle A
xₐ = v₀ₐ t + ½ aₐ t²
vehicle B
starts two seconds later
x_b = v_{ob} (t-2) + ½ a_b (t-2) ²
as cars start from rest their initial velocities are zero
at the point where they meet, the position must be the same for both vehicles
xa = 0 + ½ aₐ t²
xb = 0 + ½ a_b (t-2) ²
½ aₐ t² = ½ a_b (t-2) ²
t = (t-2)
t (1 - \sqrt{ \frac{a_a}{a_b} }) = 2
t (1 - ⅔, ) = 2
t = 2 / 0.4444
t = 45 s
b)
the speed of each car
vₐ = voa + aa t
vₐ = 0 + 2 45
vₐ = 90 m / s
v_b = 3.6 45
v_b = 162 m / s
c) xb = 0 + ½ ab (t-2) ²
x_b = ½ 3.6 (45-2) ²
x_b = 3.328 10⁴ m
Answer:
The greater the luminosity of a star, the longer its period of oscillation.
Answer:
Same direction to produce maximum magnitude and opposite direction to produce minimum magnitude
Explanation:
Let a be the angle between vectors A and B. Generally when we add A to B, we can split A into 2 sub vectors, 1 parallel to B and the other perpendicular to B.
Also let A and B be the magnitude of vector A and B, respectively.
We have the parallel component after addition be
Acos(a) + B
And the perpendicular component after addition be
Asin(a)
The magnitude of the resulting vector would be
As A and B are fixed, the equation above is maximum when cos(a) = 1, meaning a = 0 degree and vector A and B are in the same direction, and minimum with cos(a) = -1, meaning a = 180 degree and vector A and B are in opposite direction.