Respuesta :
Answer:
2.2 seconds
Step-by-step explanation:
To find the average velocity of the swimmer between 1 and 20 seconds, you can use the formula:
Average Velocity = Change in Distance/Change In Time
The change in distance (∆d) between 1 and 20 seconds is given by the difference in distance at those two times:
∆d = d(20) - d(1)
Substitute the given equation for distance (d) into the formula:
∆d = (2.2 × 20 + 7) - (2.2 × 1 + 7)
Calculate the value of ∆d, and then use the average velocity formula:
Average Velocity = ∆d/Change in Time
In this case, the change in time is
20 - 1 = 19 seconds.
Now, to find the instantaneous velocity at t = 15 seconds, you can find the derivative of the distance function with respect to time (d/dt) and evaluate it at t = 15. The derivative gives you the instantaneous velocity.
Given the distance function:
d(t) = 2.2t + 7
Take the derivative:
d/dt (d(t)) = d/dt (2.2t + 7)
The derivative is the velocity function:
v(t) = 2.2
The instantaneous velocity at t = 15 seconds is simply the value of the velocity function at that time:
v(15) = 2.2
So, the average velocity between 1 and 20 seconds can be calculated using the formula, and the instantaneous velocity at t = 15 seconds is 2.2.
