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

Answer:

The answer is "$\bold{0.36363 \ \frac{m}{s}}$"

Explanation:

Please find the attached file of the complete question:

Given:

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

Using formula:

$\to F=ma$

       $= 2.2 \ (a)\\\\= 2.2 \ \frac{dv}{dt}$

but  

$\to F= f(t)$

$\to 2.2 \ a= f(t)\\\\ \to 2.2 \ \frac{dv}{dt}=f(t)\\\\ \to \int^{v}_{0} \ dv =\int^{t= 40 ms}_{0} (\frac{f(t)}{2.2}) \ dt$

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

      $=\frac{1}{2} \times \frac{1}{2.2} \times 40 \times 40 \times 10^{-3} \ s\\\\= \frac{1}{4.4} \times 40 \times 40 \times \frac{1}{1000} \ s\\\\= \frac{1}{4.4} \times 16 \times \frac{1}{10} \ s\\\\= \frac{16}{44} \ s\\\\= 0.36363 \ \frac{m}{s}$