Question

The displacement of a body of mass 2 kg varies with time 't' as S=$t^2$+$2t$ where S is in metre and 't' is in seconds. the work done by all the forces acting on the body during the time interval t = 2s to 4s is

• A. Zero
• B. $64J$
• C. $4J$
• D. $36J$

Answer 1

Answer: (B)

$64J$

Given,

$s=t^2+2t$

$v=\frac{ds}{dt}=\frac{d}{dt}(t^2+2t)=2t+2$

$K_f=\frac{1}{2}m{v}_f^2=\frac{1}{2}\times 2\times (2\times 4+2{)}^2=100J$

$K_i=\frac{1}{2}m{v}_i^2=\frac{1}{2}\times 2\times (2\times 2+2{)}^2=36J$

$W=K_f-K_i=100-36=64J$