Question

The formula

d
=
1.3
t
2
+
t
+
2
expresses a car's distance (in feet to the north of an intersection,
d
, in terms of the number of seconds
t
since the car started to move.As the time
t
since the car started to move increases from
t
=
8
to
t
=
8.2
seconds, what constant speed must a truck travel to cover the same distance as the car over this 0.2-second interval?

Answer 1

To find the constant speed of the truck, we first determine the distance covered by the car over the 0.2-second interval by substituting values into the given formula. Then, we set up an equation to find the constant speed of the truck by equating the distance covered by the car to the distance covered by the truck in the same time interval. Solving for speed gives the answer.

Step-by-step explanation:

To find the constant speed that the truck must travel to cover the same distance as the car over the 0.2-second interval, we need to first determine the distance covered by the car during this time period. We can substitute the values of t=8 and t=8.2 into the given formula to find the distance traveled by the car:

d = 1.3t² + t + 2

For t=8, the car's distance is:

d = 1.3(8)² + 8 + 2 = 94.2 feet

For t=8.2, the car's distance is:

d = 1.3(8.2)² + 8.2 + 2 = 101.768 feet

The difference in distance covered by the car over this 0.2-second interval is:

101.768 - 94.2 = 7.568 feet

Now, we can set up an equation to find the constant speed of the truck:

distance = speed x time

The truck must cover the same distance of 7.568 feet in the 0.2-second interval, so:

7.568 = speed x 0.2

Solving for speed:

speed = 7.568 / 0.2 = 37.84 feet per second

Answer 2

The truck travel must to have a constant speed of
`22.06\ ft/sec`

Step-by-step explanation:

we have

`d=1.3t^(2)+t+2`

where

d expresses a car's distance in feet

t is the number of seconds

Find the distance d for t=8 sec

`d=1.3(8)^(2)+8+2=93.2\ ft`

Find the distance d for t=8.2 sec

`d=1.3(8.2)^(2)+8.2+2=97.612\ ft`

The total distance in this interval of 0.2 sec is

`97.612-93.2=4.412\ ft`

Find the speed of the car

Divide the total distance by the time

`4.412/0.2=22.06\ ft/sec`

therefore

The truck travel must to have a constant speed of
`22.06\ ft/sec`