Answer:
LHS=RHS=[L]
Explanation:
Given mathematical expression:
where: dimension:
s = displacement length
u = initial velocity
t = time
a = acceleration
now using dimensional analysis:
we know that the ratio and constants have no dimension.
as we know that only similar dimensions can be added or subtracted therefore we get a correct conclusion.
<em>However we can deduce the operators between the equations and can neither check for the validity of the constants. We can only check for the dimension of the terms involved.</em>
Answer:
The travel would take 6.7 years.
Explanation:
The equation for an object moving in a straight line with acceleration is:
x = x0 + v0 t + 1/2a*t²
where:
x = position at time t
x0 = initial position
v0 = initial velocity
a = acceleration
t = time
In a movement with constant speed, a = 0 and the equation for the position will be:
x = x0 + v t
where v = velocity
Let´s calculate the position from the Earth after half a year moving with an acceleration of 1.3 g = 1.3 * 9.8 m/s² = 12.74 m/s²:
Seconds in half a year:
1/2 year = 1.58 x 10⁷ s
x = 0 m + 0 m/s + 1/2 * 12.74 m/s² * (1.58 x 10⁷ s)² = 1.59 x 10¹⁵ m
Now let´s see how much time it takes the travel to the nearest star after this half year.
The velocity will be the final velocity achived after the half-year travel with an acceleration of 12.74 m/s²
v = v0 + a t
Since the spacecraft starts from rest, v0 = 0
v = 12.74 m/s² * 1.58 x 10⁷ s = 2.01 x 10 ⁸ m/s
Using the equation for position:
x = x0 + v t
4.1 x 10¹⁶ m = 1.59 x 10¹⁵ m + 2.01 x 10 ⁸ m/s * t
(4.1 x 10¹⁶ m - 1.59 x 10¹⁵ m) / 2.01 x 10 ⁸ m/s = t
t = 2.0 x 10⁸ s * 1 year / 3.2 x 10 ⁷ s = 6.2 years.
The travel to the nearest star would take 6.2 years + 0.5 years = 6.7 years.
The sun is a star, not a planet. Jupiter is the biggest planet in the solar system. :)
Answer:
d = 114.95 m
Explanation:
Givens:
a = 7.6 m/s^2
t = 5.5 s
v_i = 0 m/s
a = (v_f-v_i)/t
7.6 m/s^2 = (v_f-0 m/s)/5.5 s
v_f = (7.6 m/s^2)*(5.5 s)
v_f = 41.8 m/s
d = [(v_f+v_i)/2]*t
d = [(41.8 m/s)/2]*5.5 s
d = 114.95 m
Answer:
The product of mass and velocity is the correct answer
Explanation:
Momentum is defined as mass × velocity
p = mv