A body start with an initial velocity of 10metre per second move along the straight line with constant acceleration and the velocity of the body is 50 metre per second the acceleration is reversein the direction find the velocity of the particle as it reach the starting point

To find the velocity of the particle as it reaches the starting point, we need to determine the acceleration and the time it takes for the body to reach the starting point.

Let's assume the initial velocity of the particle is positive (+10 m/s) and the acceleration is negative (-a), since it is reverse in direction.

First, let's calculate the time it takes for the particle to reach the velocity of 50 m/s:
Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Given:
u = 10 m/s
v = 50 m/s
a = -a (negative acceleration)

50 = 10 + (-a)t
40 = (-a)t

Now, let's determine the time it takes for the particle to reach the starting point.
Since the acceleration is negative, the particle will decelerate until it comes to a stop (0 m/s). At this point, it will reverse direction and accelerate back towards the starting point.

To find the time it takes for the particle to reach 0 m/s, we can use the equation:
v = u + at

Given:
u = 50 m/s
v = 0 m/s
a = -a (negative acceleration)

0 = 50 + (-a)t
(-a)t = -50

Now, since the particle needs to reach the starting point, it will take the same amount of time to go from 0 m/s to the negative initial velocity (-10 m/s). So, we can write the equation as:

(-a)t = -50 = 10

Now we can solve for t:
t = 10/a

To find the velocity of the particle as it reaches the starting point, we use the equation:
v = u + at

Given:
u = -10 m/s (negative initial velocity)
a = -a (negative acceleration)
t = 10/a

v = (-10) + (-a)(10/a)
v = -10 - 10
v = -20 m/s

Therefore, the velocity of the particle as it reaches the starting point is -20 m/s.

To find the velocity of the particle as it reaches the starting point, we need to use the kinematic equation:

v = u + at

Where:
v = final velocity (50 m/s)
u = initial velocity (10 m/s)
a = acceleration
t = time

Since the particle is returning to its starting point, the displacement is 0. Therefore, we can use the equation:

v^2 = u^2 + 2as

Where:
s = displacement

Since s = 0, the equation becomes:

v^2 = u^2

Rearranging the equation to solve for the final velocity:

v = √(u^2)

v = √(10^2)
v = √100
v = 10 m/s

Therefore, the velocity of the particle as it reaches the starting point is 10 m/s.