Question

The velcity of a paarticle is given by v=u_(0) + gt+ 1/2 ft^(2). If its position is `x =0` at `t=0`, then what is its displacement after `t=1 s` ?
A. `v_(0) +g//2+f`
B. `v_(0) +2 g+3f`
C. `v_(0) +g//2 +f//3`
D. `v_(0) +g +f`

Answer 1

Correct Answer - C
`v = v_(0) +g t +ft^(2)`
or `(dx)/(dt) = v_(0) +g t +ft^(2)`
`rArr dx = (v_(0) +gt +ft^(2)) dt`
So, `int_(0)^(x) dx = int_(0)^(1) (v_(0) +gt +ft^(2))dt`
`rArr x = v_(0) +(g)/(2) +(f)/(3)`