Question

A child pushes a 2.2kg swing that is initially at rest. The net force on the swing over time is shown below. What's the swings speed at t= 40ms

Answer 1

The answer is "
`\bold{0.36363 \ (m)/(s)}`"

Step-by-step explanation:

Please find the attached file of the complete question:

Given:

`m= 2.2 \ kg\\\\t= 40 \ ms`

Using formula:

`\to F=ma`

`= 2.2 \ (a)\\\\= 2.2 \ (dv)/(dt)`

but

`\to F= f(t)\\\\`

`\to 2.2 \ a= f(t)\\\\ \to 2.2 \ (dv)/(dt)=f(t)\\\\ \to \int^(v)_(0) \ dv =\int^(t= 40 ms)_(0) ((f(t))/(2.2)) \ dt\\\\`

`\to v= \frac{\text{(Area of given graph)}} {2.2} \\\\`

`=(1)/(2) * (1)/(2.2) * 40 * 40 * 10^(-3) \ s\\\\= (1)/(4.4) * 40 * 40 * (1)/(1000) \ s\\\\= (1)/(4.4) * 16 * (1)/(10) \ s\\\\= (16)/(44) \ s\\\\= 0.36363 \ (m)/(s)`