Question

A train is travelling down a stright track when the engineer applies at 10ms the brakes, resulting in an acceleration of -1.0ms as long as the train is in motion. How far does the train move during a 10s time interval Starting at the instant breaks applied?​

Answer 1

To determine the distance the train moves during a 10-second time interval after the brakes are applied, we can use the equation of motion:

d
=
v
i
t
+
1
2
a
t
2
d=v
i
​
t+
2
1
​
at
2


where:
d is the distance,
v
i
v
i
​
is the initial velocity,
a is the acceleration, and
t is the time.

Given:
v
i
=
10
 
m/s
v
i
​
=10m/s (initial velocity),
a = -1.0 m/s² (acceleration),
t = 10 s (time interval).

Substituting the given values into the equation, we have:

d
=
(
10
 
m/s
)
(
10
 
s
)
+
1
2
(
−
1.0
 
m/s
2
)
(
10
 
s
)
2
d=(10m/s)(10s)+
2
1
​
(−1.0m/s
2
)(10s)
2


Simplifying the equation, we get:

d
=
100
 
m
−
50
 
m
d=100m−50m

Therefore, the train moves a distance of 50 meters during the 10-second time interval starting when the brakes are applied.