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?

It takes the train 7.5 seconds to reach top speed

The train travels 112.5 meters before it reaches its top speed

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;

→

→ 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

this could be newton#'s law of cooling. the cooling curve is exponential