Velocity Problems And Solutions

Introduction:

Normally rate of change of position in math is known as velocity.  It is one of the vector quantities because when we mentioned the velocity it will indicate the direction also. Velocity is normally defined by the ratio between the distance and time. In velocity problems we can measure the time and distance. Velocity problems are used to find the solutions for the distance problems. We can find the solutions for maximum height of the object traveled. velocity problems and solutions are one of the main application in physics.

Velocity problems and solutions:


Problem 1:

    A submarine descends 90 miles in 10 seconds. Find the velocity of the submarine.

Solution:

Step1:

    We know the velocity formula V = Distance (d) / Time (t)

Step2:

   Here distance d = 90 miles

  And the time t = 10 seconds.
Here the submarine is descending so the velocity will be negative velocity.

Step 3:

 So velocity = - 90 / 10 miles / sec

 Velocity V = - 9 miles / sec.

We can find the distance travelled by the object using the velocity problems.


Problem 2:


   A ball is thrown upwards in the air from the ground. The distance travelled by the ball is

 h = 16t2 - 64t + 6. Find the maximum height of the ball.

Solution:

 The distance traveled by the ball is h = 16t2 - 64t + 6

 We want to find the maximum height. When the ball is maximum height the velocity will be zero. To find the velocity function we have to differentiate the distance function with respect to t.
 V = d h / d t = d / d t (16t2 - 64t + 6)

   V = d h / d t =32t - 64

   If the ball is at maximum height velocity v = 0         

   32t - 64 = 0

    32t = 64

   t = 64 / 32

   t = 2

   So when time t = 2 the ball will beat maximum height.

   h = 32 (2)2 -64(2) + 6

  h = 128 – 128 +6

 h = 6           

From the above problem we used the velocity to find the solutions for the maximum height.