Question

Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determined by the equation d = 144 – 16t2, where t is the number of seconds it takes the car to travel down to each point on the ride. For which interval of time is Greg’s car moving in the air?

Answer 1

time is 3
Interval : 0 < t < 3

Answer 2

The distance(d), of the car from the ground as the car descends is determined by the equation

`d = 144 -16t^2`

where t is the number of seconds it takes the car to travel down to each point on the ride.

We have to find the interval of time is Greg’s car moving in the air.

⇒
`d > 0`

⇒
`144 -16t^2 > 0`

⇒
`144 > 16t^2`

Divide both sides by 16 we get;

`9 > t^2`

⇒
`t < \pm 3`

Since, t is the tim, it cannot be in negative,
`t > 0`

⇒
`t < 3`

Therefore, the interval for which Greg’s car moving in the air is,

0<t<3 or (0, 3)