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 s is
(1) 5m
(2) 15m
(3) 25 m
(4) 50 m​

Answer 1

Answer:

$\bold\red{x_{10\:s}= 0\:metres}$

Explanation:

Given,

Velocity of a particle as function of time,

V = 5 - t

We know that,

Velocity, V = dx/dt

where, x is displacement .

Thus, we may write,

$\frac{dx}{dt} = 5 - t \\ \\ = > dx = (5 - t)dt$

To get, the displacement,

we must integrate the following equation.

Thus,

$= > \int \: dx = \int(5 - t)dt \\ \\ = > x = 5t - \frac{ {t}^{2} }{2}$

Thus,

we got the displacement as a function of time

Therefore,

Displacement in 10 seconds is,

$=>x_{10\:s}= 5×10 - \frac{{10}^{2}}{2}$

$=>x_{10\:s}= 50 - \frac{100}{2}$

$=>x_{10\:s}= 50- 50$

Hence,

$=>x_{10\:s}= 0\:metres$

Answer 2

Answer:

may be answer is 50m..

As,

t = 10s

v = 5 - t (m/s)

= 5 - 10

= 5m/s

V = S ÷ T

S = V × T

= 5 × 10

= 50 m