suppose a treadmill has an avg acceleration of 4.7m/s^2.

a) how much does its speed change after 5 min?
b) If the treadmill's initial speed is .017 km/s, what will it's final speed be?

That is half a g for 5 minutes, way too gigantic but anyway

v = Vi + a t
here t = 5 * 60 = 300 seconds

To answer these questions, we can use the equations of motion associated with acceleration.

a) To find how much the speed changes after a certain time, we can use the equation:

Δv = a * t

where:
Δv = change in velocity (speed)
a = acceleration
t = time

In this case, the given acceleration is 4.7 m/s^2, and the time is 5 minutes. However, it's important to note that the time should be converted to seconds since the acceleration is given in m/s^2. Therefore, 5 minutes can be converted to 300 seconds (1 minute = 60 seconds).

Substituting the values into the equation:

Δv = 4.7 m/s^2 * 300 s
Δv = 1410 m/s

So, the speed changes by 1410 m/s after 5 minutes.

b) To find the final speed, we need to consider the initial speed and the change in speed. We can use the equation:

v = u + Δv

where:
v = final speed
u = initial speed
Δv = change in velocity (speed)

In this case, the initial speed is given as 0.017 km/s. To convert it to m/s, we multiply by 1000 (1 km = 1000 m).

u = 0.017 km/s * 1000 m/km
u = 17 m/s

We already calculated the change in speed (Δv) as 1410 m/s. Substituting the values into the equation:

v = 17 m/s + 1410 m/s
v = 1427 m/s

So, the final speed of the treadmill would be 1427 m/s.