The velocity of a car (in miles per hour) is given by
v(t) = 61.25t − 17.5 t^2
where t is in hours. Write a definite integral for the distance the car travels during the first 2.5 hours. Use your graphing calculator to find this distance.
Distance =
d = 61.25 t^2/2 - 17.5 t^3/3 + 0
if t = 2.5
d = 191.4 - 91.1 = about 100 miles
To find the distance the car travels during the first 2.5 hours, we need to find the integral of the velocity function over the interval [0, 2.5].
The definite integral is given by:
∫[0,2.5] (61.25t - 17.5 t^2) dt
Now, let's use a graphing calculator to find this distance.
To find the distance traveled by the car during the first 2.5 hours, we need to integrate the velocity function with respect to time from 0 to 2.5.
The definite integral for the distance is given by:
∫[0 to 2.5] (61.25t − 17.5t^2) dt
To find this distance using a graphing calculator, you would need to follow these steps:
1. Open your graphing calculator and go to the home screen.
2. Press the "Math" button or the "CALC" button, depending on your calculator model.
3. Select the option for definite integral, often represented as "∫".
4. Enter the function as "61.25t - 17.5t^2" after the integral symbol.
5. Specify the variables and the limits of integration, in this case, "t" from 0 to 2.5.
6. Press the "Enter" or "Calculate" button to find the result.
After performing these steps, your graphing calculator should give you the numerical value of the distance the car travels during the first 2.5 hours.
Note: The exact procedure may vary depending on the model and brand of your graphing calculator. Please consult the user manual or online resources specific to your calculator for detailed instructions.