suppose a treadmill has an average acceleration of 4.7 x 10^-3 m/s^2.

a. how much does its speed change after 5.0 min?
b. if the treadmill's initial speed is 1.7 m/s, what will its final speed be?

a. The treadmill's speed after 5.0 min will change so much that it might even consider joining a speed dating event. But seriously, to calculate the change in speed, we can use the formula:

Δv = a * t

where Δv is the change in velocity, a is the acceleration, and t is the time. Plugging in the given values:

Δv = (4.7 x 10^-3 m/s^2) * (5.0 min * 60 s/min)

Calculating that, you'll find the change in speed after 5.0 min on the treadmill.

b. Now, if the initial speed of the treadmill is 1.7 m/s and we want to find the final speed after a certain time, we can again use the formula:

vf = vi + Δv

where vf is the final velocity, vi is the initial velocity, and Δv is the change in velocity. Plugging in the values:

vf = 1.7 m/s + Δv

We already calculated Δv in part a, so you can add that to the initial speed to find the final speed of the treadmill. Keep in mind that Δv might have changed, depending on the time specified, so recalculate it if needed.

To solve these problems, we can use the equations of motion, specifically the equation that relates acceleration (a), initial velocity (v₀), final velocity (v), and time (t):

v = v₀ + at

a. To find how much the speed changes after 5.0 minutes, we need to calculate the final velocity (v) after this time. We know the initial velocity (v₀) is zero (since the treadmill starts from rest). We also know the time (t) is 5.0 minutes, but we need to convert it to seconds because the acceleration is given in m/s^2:

t = 5.0 minutes = 5.0 * 60 seconds
t = 300 seconds

Now, we can use the equation of motion to find the final velocity (v):

v = v₀ + at
v = 0 + (4.7 x 10^-3) * 300
v ≈ 1.41 m/s

So, the speed of the treadmill changes by approximately 1.41 m/s after 5.0 minutes.

b. To find the final speed of the treadmill, we need to add the change in speed (calculated in part a) to the initial speed (v₀):

Final speed (v) = Initial speed (v₀) + Change in speed

v = 1.7 m/s + 1.41 m/s
v ≈ 3.11 m/s

Therefore, the final speed of the treadmill will be approximately 3.11 m/s.

Student

a. (acceleration)*(time in seconds)

= 4.7*10^3*300 = 1.41 m/s

b. (initial speed) + (speed change) = ? m/s
= 1.7 + (answer of part a)= ?