A particle is moving in a straight line with initial velocity and uniform acceleration a. If the sum of the distance travelled in and seconds is , then its velocity after seconds, in , is
Step 1. Given data
The sum of the distance travelled in and seconds is .
We have to find the velocity.
Step 2. Concept used.
The distance travelled in second is,
-----------
Here, is the distance travelled time, is the initial velocity, and is acceleration of the body in motion.
Step 3. Calculate the velocity.
The distance travelled in and second is .
Now we will find the sum of distances.
By using the expression , the distance travelled in is,
------
And the distance travelled in is,
----------
According to the given, the total distance travelled in and second is , so, we have to add expression and , we get,
Substitute the values of expression and in above expression, we get,
------
Now, from the first equation of motion the velocity of any particle after time , if it moves with acceleration is,
--------
Now, its clear that is similar in expression as well as , so substitute the value of from expression in , we get
Hence, a particle is moving in a straight line with initial velocity and uniform acceleration a. If the sum of the distance travelled in and seconds is , then its velocity after seconds, in , is .