Question

As a train enters the station it slows down from 40 m/s to a 10 m/s in 5 seconds

1 what is the acceleration of the train

2 how far does the train travel during this time

Answer 1

See the answers below.

Step-by-step explanation:

To solve this problem we must use the following equation of kinematics.

`v_(f)=v_(o)-a*t`

where:

Vf = final velocity = 10 [m/s]

Vo = initial velocity = 40 [m/s]

t = time = 5 [s]

a = acceleration [m/s²]

Now replacing:

`10=40-a*5\\40-10=a*5\\30=5*a\\a=6[m/s^(2)]`

Note: The negative sign in the above equation means that the velecity is decreasing.

2)

To solve this second part we must use the following equation of kinematics.

`v_(f)^(2) =v_(o)^(2) -2*a*x\\`

where:

x = distance [m]

`(10)^(2) =(40)^(2) -2*6*x\\100=1600-12*x\\12*x=1600-100\\12*x=1500\\x=125[m]`