To calculate the distance traveled by the particle in the 5th second of its motion, we need to determine the time it takes for the particle to come to a stop and then calculate the distance covered during that time.
The given information provides the initial velocity (u = 10 m/s) and the retardation (a = -2 m/s^2). The negative sign indicates retardation or deceleration.
Using the equation of motion:
v = u + at
where: v = final velocity (when the particle comes to a stop) u = initial velocity a = acceleration (retardation in this case) t = time
We can rearrange the equation to solve for the time it takes for the particle to come to a stop:
v = u + at 0 = 10 + (-2)t -10 = -2t t = 5 seconds
Therefore, the particle comes to a stop at t = 5 seconds.
To calculate the distance traveled during this time, we can use the equation of motion:
s = ut + (1/2)at^2
where: s = distance traveled u = initial velocity t = time a = acceleration (retardation in this case)
Plugging in the values:
s = (10)(5) + (1/2)(-2)(5)^2 s = 50 - 25 s = 25 meters
Therefore, the distance traveled by the particle in the 5th second of its motion is 25 meters.