Question

The velocity of a point moving in straight line is V = (12t-3t2) m/s. Find the path covered by the point from the begining of motion to the instant of stop.​

Answer 1

Given , V =  ( 12t - 3t² )m/s .

first let us find the time at which the point stops i.e., velocity is zero.

⇒  V =   ( 12t - 3t² ) = 0

   ⇒  3t ( 4 -t ) = 0

   ⇒ t = 0 or t = 4 sec.

so ,  the point stops after 4 seconds from the start.

Now we know that   ( ds / dt ) = V  ; where s is the distance covered by the point .  

⇒  ( ds / dt ) = V

⇒  ds = V . dt   ⇒   ds  =  ( 12t - 3t² ) . dt      

              (on integrating)

⇒      $\int\limits^4_0 {s} \, =$     $\int\limits^4_0 {( 12t - 3t^{2} ) } \, dx$

⇒    $s = [ \frac{12tx^{2} }{2} - \frac{3t^3}{3} ]$

⇒       s = 32 m.

∴ the path covered by the point from the begining of motion to the instant of stop is 32 m .

Hope this helps you ✌️✌️☘️☘️.