Question

9. The Metro Rail makes a stop at NRG Stadium to pick up some Texans fans after the game. After

all the passengers board, the train accelerates at a rate of 4 m/s? to a top speed of 30 m/s. How
long does it take for the train to reach top speed? How far does it travel before it reaches its top
speed?

Answer 1

It takes the train 7.5 seconds to reach top speed

The train travels 112.5 meters before it reaches its top speed

Step-by-step explanation:

The Metro Rail makes a stop at NRG Stadium to pick up some Texans

fans after the game

After all the passengers board, the train accelerates at a rate of 4 m/s²

to a top speed of 30 m/s

We need to find the train takes how many seconds to reach the

top speed

Given is:

→ The train start from rest, then its initial speed u = 0

→ It acceleration a = 4 m/s²

→ Its top speed v = 30 m/s

To find the time we can use this rule;

→
`t=(v-u)/(a)`

→
`t=(30-0)/(4)=(30)/(4)=7.5` seconds

It takes the train 7.5 seconds to reach top speed

Now we need to find how far the train travels before reaches top speed

We can use this rule;

→ v² = u² + 2as, where s is the distance

→ v = 30 m/s , u = 0 , a = 4 m/s²

Substitute these values in the rule

→ (30)² = 0 + 2(4) s

→ 900 = 8 s

Divide both sides by 8

→ s = 112.5 m

The train travels 112.5 meters before it reaches its top speed