Distance travelled by a given body in a given time

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Q. Distance travelled by a body in motion in a given time

State how the velocity-time graph can be used to find
(i) the acceleration of a body,
(ii) the distance travelled by the body in a given time, and
(iii) the displacement of the body in a given time.

Q. The position of a body moving along

x -

axis at time

t

is given by

x = (t^{2} - 4 t + 6) m

. The distance travelled by body in time interval

t = 0

t = 3

s is

Q. The equation of motion of a body falling under gravity is given by

\frac{d v}{d t} = g - \frac{g}{λ^{2}} v^{2}

. Distance travelled as a function of time is given by?. Give at

v = 0

t = 0

Q. The differential equation of a body projected from the earth is given by

\frac{d v}{d t} = - g - k v

.The distance travelled by the body at any time

t

is given by

x = (\frac{g}{k^{2}} + \frac{u}{k}) (1 + e^{- k t}) - \frac{g}{k} t

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