Question

# A particle having initial velocity ( u ) moves with a constant acceleration a for a time t. (a) Find the displacement of the particle in the last 1 second. (b) Evaluate it for ( u equiv 5 mathrm{m} / mathrm{s}, a=2 mathrm{m} / mathrm{s}^{2} ) and ( t equiv 10 mathrm{s} )

Solution

S ( frac{1}{2} ) at ( frac{1}{2} ) at ( ^{2} )

a) Disflacement in last one suond

( =S_{t}-S_{t-1} )

( =left(u+frac{1}{2} a t^{2}right)-left(u(t-1)+frac{1}{2} a(t-1)^{2}right) )

( =ut-ut+u+frac{1}{2} aleft(t^{2}-(t-1)^{2}right) )

( =frac{1}{2}+frac{1}{2} a(t-t+1)(t+t-1) )

(u + frac{1}{2} a (2t - 1))

b) displament in last one secosecond

(5 + frac{1}{2} times 2 (20 -1) = 5 + 19)

( =24 mathrm{m} )