Question

A `100 g ` block moves along `X-` axis. Its acceleration as a function of displacemetn is shown in figure. Calculate work done (in joule) on the block by the force applied as the block moves from `x=0` to `x=8m`.

Answer 1

As the given graph is linear , figure,
`:. a = alphax, ` where` alpha` is slope of graph
`alpha=(a)/( x)=(20)/(8)=2.5s^(-2)`
Now, `F=ma=m alpha x`
`W=int _(0)^(8)F dx = int _(0)^(8)m alpha x dx = m alpha [(x^(2))/( 2)]_(0)^(8)`
`=(2.5)/(10)((64-0)/(2))=8J`