A particle starts from origin with uniform acceleration. Its displacement after t seconds is given in metres by the relation `x = 2 + 5 t + 7t^2`
Calculate the magnitude of its (i) initial velocity (ii) velocity at t =4 s (iii) uniform acceleration (iv) displacement at t =5 s.

Answer

(i) `5m//s` (ii) `61m//s` (iii) `14m//s^2` (iv) 202 m

Explanation

Velocity, `upsilon = (dx)/(dt) = (d)/(dt) (2+5t +7t^2) =(5 +14t)`
(i) When `t =0, upsilon = 5m//s` (ii) When `t =4 s, upsilon =5 +14 xx4 =61m//s`
(iii) Acceleration, `a=(dv)/(dt) = (d)/(dT) (5+14t) = 14m//s^2`
(iv) When `t =5s, x =2 +5xx5+7xx5^2 = 2 +25 +175 =202m`