Question

If velocity v of a particle moving on a straight line
as a function of time t is given as v = 5 - t (m/s)
then the distance covered by the particle in first 10 sec is (1)5m
(2) 15 m
(4) 50 m
(3)25 m​

Answer 1

Answer:

25m

Explanation:

v = 0 at t = 5s

v = 5 - t = dx/dt

dx = (5-t) dt

Intergrating,

x = 5t - t^2 / 2

1) t  = 5

x = 25/2

2) t = 10

x = 0

So particles moves from 0 to 25/2 then from 25/2 to 0

So distance = 25/2 + 25/2 = 25m

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Answer 2

v = 5-t

We know,

v = dx/dt = 5-t

It can be written as,

dx = 5-tdt

Integrating both sides we get,

x = 5t-t²/2

Taking t = 5seconds,

x = 5×5 -25/2 = 25-25/2 = 25/2 = 12.5m

Taking t = 10s

x = 5×10-10²/2 = 0m

So, in whole period of time object goes from start to that is 0 to 12.5m and from 12.5m again to 0m

It's distance will be = 12.5+12.5 = (3)25m

Its displacement however will be Zero.

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