Question

The formula d = 1.1 t 2 + t + 1 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 = 3 to t = 5 seconds, what constant speed must a truck travel to cover the same distance as the car over this 2-second interval?

Answer 1

To find the constant speed the truck must travel to cover the same distance as the car from t = 3 to t = 5 seconds, calculate the distance the car covers during this interval using the given distance formula and divide it by the time interval, resulting in a constant speed of 9.8 feet per second for the truck.

Step-by-step explanation:

To determine the constant speed the truck must travel to cover the same distance in the same time interval as the car, we first calculate the distance the car travels from t = 3 to t = 5 seconds using the given equation for distance d = 1.1t2 + t + 1.

First, find the distance at t = 5 seconds:
d(5) = 1.1(5)2 + (5) + 1 = 1.1(25) + 5 + 1 = 27.5 + 5 + 1 = 33.5 feet.

Now find the distance at t = 3 seconds:
d(3) = 1.1(3)2 + (3) + 1 = 1.1(9) + 3 + 1 = 9.9 + 3 + 1 = 13.9 feet.

Next, calculate the distance traveled by the car between t = 3 seconds and t = 5 seconds:
Distance traveled = d(5) - d(3) = 33.5 feet - 13.9 feet = 19.6 feet.

Since this distance is traveled in a 2-second interval, the truck's constant speed must be the total distance divided by time:
Speed = Total distance / Time interval = 19.6 feet / 2 seconds = 9.8 feet per second.

Therefore, the truck must travel at a constant speed of 9.8 feet per second to cover the same distance as the car in the 2-second interval.