Question

The table below represents the velocity of a car as a function of time: Time (seconds) x Velocity (m/s) f (x) 15 45 22 66 29 87 36 108 The average rate of change of the function between x = 15 to x = 29 is 87 m/s2 and represents the car's acceleration.

Answer 1

The velocity of the car at various times is given as:

Velocity at 15 seconds = f(15) = 45
Velocity at 22 seconds = f(15) = 66
Velocity at 29 seconds = f(15) = 87
Velocity at 36 seconds = f(15) = 108

We are to find the average rate of change of f(x) from x=15 to x=29, which can be written as:

$\frac{f(29)-f(15)}{29-15} \\ \\ = \frac{87-45}{14} \\ \\ = \frac{42}{14} \\ \\ =3$

Therefore, the average rate of change of function from x=15 to x=29 is 3. Since the rate of change of velocity gives us acceleration, so the acceleration of the car between 15 to 29 seconds will be 3 m/s²

Answer 2

Answer: 3

Step-by-step explanation: