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 is

Answer 1

Answer:

$G( t ) = -\dfrac{\left(t-10\right)t}{2} + C$

Explanation:

Let S be the function of time which returns the velocity,

$S( t ) = 5 - t$

Now, distance ( actually displacement in this case ) is the product of velocity and time.

We plot the velocity-time graph ( attached with the answer ), the area under the line is the displacement. That's simple integration of S( t ). Let t = x.

$\int S( x ) \  dx  \\= \int ( 5 - x )\\= 5 \int 1 \ dx - \int x \ dx\\= 5x - \frac{x^2}{2} + C$

Let the above function be G,

$G( t ) = -\dfrac{\left(t-10\right)t}{2} + C$

Returns the displacement given time ( t ).