Initial speed = 2√10 m/s
<h3>Further explanation </h3>Linear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration
An equation of uniformly accelerated motion
V = vo + at
Vt² = vo² + 2a (x-xo)
x = distance on t
vo / vi = initial speed
vt / vf = speed on t / final speed
a = acceleration
vf=20 m/s
d = 60 m
a = 3 m/s²
The time needed for the 7th car to pass is 13.2 s
Explanation:
The motion of the train is a uniformly accelerated motion, therefore we can use suvat equations.
We start by analzying the motion of the first car, by using the equation:
where
s is the distance covered by the first car in a time t, which corresponds to the length of one car
u = 0 is the initial velocity
a is the acceleration
t = 5.0 s is the time
The equation can be rewritten as
where L is the length of one car.
The same equation can be written considering the first 7 cars:
where
7L is the distance covered by the 7 cars
t' is the time needed
We still have
u = 0
And the acceleration is constant so it is
Substituting into the equation, we can find t':
In attachment the graph of the distance covered versus the time taken: since the motion is uniformly accelerated, the relationship between the two variables is quadratical.
Learn more about accelerated motion:
#LearnwithBrainly
Answer:
A) 1.67 x 10 ⁻⁶ m/s
B)5.59 x %
Explanation:
A)
Given:
d = 5.0 km,
mₐ = 2.5 x kg
u₁ = 4.0 x 10⁴ m/s
= 5.98 x 10 ²⁴ kg
Solve using kinetic conserved energy
mₐ x u₁ + x u₂ = uₓ x (mₐ +
)
(2.5 x ) (4.0 x 10⁴ )+ (5.98 x 10 ²⁴ )(0) = uₓ x (2.5 x
+ 5.98 x 10 ²⁴ )
uₓ = ( 2.5 x x 4.0 x 10⁴ ) / (2.5 x
+ 5.98 x 10 ²⁴ )
uₓ = 1.67 x 10 ⁻⁶ m/s
B) Assuming earth radius as a R = 1.5 x 10 ¹¹ m
t = 365 days x 24 hr / 1 day x 60 minute / 1 hr x 60s / 1 minute = 31536000 s
t = 31536000 s
D = 2 π R = 2 π( 1.5 x 10 ¹¹ )
D = 9.4247 x 10 ¹¹ m
u₂ = D / t = 9.4247 x 10 ¹¹ / 31536000
u₂ = 29885.775 m/s
% = ( 1.67 x 10 ⁻⁶ m/s ) / (29885.775 m/s) x 100
% = 5.59 x %