Question

A train travelling at 20m/s undergoes a uniform deceleration of 2m/s2 when brakes are applied.. calculate the time taken to come to rest and distance travel from the place where the brakes were applied ​

Answer 1

a) 10 seconds

b) 100 meters

Step-by-step explanation:

Accelerated Motion

If an object is moving at contant speed, we know it has zero net force applied. As soon as an unbalanced force appears, the object accelerates (positive or negative) depending on the direction of the force with respect to movement. The speed of an object subject to acceleration is given by

`v_f=v_o+at`

The distance traveled is given by

`\displaystyle x=v_ot+(at^2)/(2)`

a)

Our train is travelling at 20m/s when it decelerates at
`-2\ m/s^2` (negative for it's against movement). If nothing else happens, it will eventually stop (
`v_f=0`). We can compute the time at which it happens :

`\displaystyle t=(v_f-v_o)/(a)`

`Knowing\ v_f=0`

`\displaystyle t=(-20)/(-2)=10\ sec`

b)

The distance traveled is

`\displaystyle x=v_ot+(at^2)/(2)`

`\displaystyle x=(20)(10)-(2(10)^2)/(2)`

`\displaystyle x=100\ m`