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3 years ago

6

A train, traveling at a constant speed of 22.0 m/s, comes to an incline with a constant slope. While going up the incline, the t

rain slows down with a constant acceleration of magnitude 1.40 m/s2. How far has the train traveled up the incline after 7.30 s

2 answers:

Alexus [3.1K]3 years ago

6 0

Answer:

123.297 m

Explanation:

A train, traveling at a constant speed of 22.0 m/s,

v = 22.0 m/s

the train slows down with a constant acceleration of magnitude 1.40 m/s².

$a_s$ = -1.4 m/s²

How far has the train traveled up the incline after 7.30 s

t =7.30 s

We can calculate the distance traveled up the incline after 7.30 s by using the formula:

$x_f =x_i+v_xt+\frac{1}{2}a_st^2$

where;

$x_f$ = the distance traveled up

$x_i$ = 0

$v_x$ = speed of the train

$a_s$ = deceleration

t = time

Substituting our data; we have:

$x_f = 0+(22m/s)(7.30s)+\frac{1}{2}(-1.4m/s^2)(7.30s)$

$x_f =16.06 -37.303$

$x_f$ = 123.297 m

Charra [1.4K]3 years ago

4 0

Answer:

123.30 m

Explanation:

Given

Speed, u = 22 m/s

acceleration, a = 1.40 m/s²

time, t = 7.30 s

From equation of motion,

v = u + at

where,

v is the final velocity

u is the initial velocity

a is the acceleration

t is time

V = at + U

using equation v - u = at to get line equation for the graph of the motion of the train on the incline plane

$V_{x} = mt + V_{o}$ where m is the slope

Comparing equation (1) and (2)

$V = V_{x}$

a = m

$U = V_{o}$

Since the train slows down with a constant acceleration of magnitude 1.40 m/s² when going up the incline plane. This implies the train is decelerating. Therefore, the train is experiencing negative acceleration.

a = - 1.40 m/s²

Sunstituting a = - 1.40 m/s² and u = 22 m/s

$V_{x} = -1.40t + 22$

$V_{x} = -1.40(7.30) + 22$

$V_{x} = -10.22 + 22$

$V_{x} = 11. 78 m/s$

The speed of the train at 7.30 s is 11.78 m/s.

The distance traveled after 7.30 sec on the incline is the area cover on the incline under the specific interval.

Area of triangle + Area of rectangle

$[\frac{1}{2} * (22 - 11.78) * (7.30)] + [(11.78 - 0) * (7.30)]$

= 37.303 + 85.994

= 123. 297 m

≈ 123. 30 m

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