Question

Suppose a treadmill has an average accelera- tion of 0.0039 m/s2. How much does its speed change after 4.1 min? Answer in units of m/s.

Answer 1

Speed change = (final speed) - (initial speed)

Final speed = (initial speed) + (acceleration) x (time)

So Speed change = (acceleration) x (time)

(4.1 min) x (60 sec /min) = 246 seconds

Speed change = (0.0039 m/s²) x (246 seconds)

Speed change = 0.96 m/s

Answer 2

To solve this problem, we should first convert all quantities to SI units. The one quantity that is not in SI units is the time. We can convert 4.1min into seconds by multiplying by 60s as follows,

`4.1min = (60s)/(min) *4.1min=246s.`

Average acceleration is defined as,
`a=\tfrac{\Delta v}{\Delta t}`

where
`\Delta v` is the change in velocity and
`\Delta t` is the change in time. To find the speed after a given time, we have to solve for the change in speed in the equation for acceleration. The change is speed is,

`\Delta v=a\cdot \Delta t`.

From this we can now calculate the change in speed as follows,

`\Delta v = a\Delta t =0.0039m/s^2* 246s= 0.9594m/s.`

Since the speed increases from zero, the change in speed of
`0.9594m/s` is the speed after 4.1min.