A particle accelerates uniformly from rest at 6.oms for 8s and then decelerates uniformly to rest in the next 5s. determine the magnitude of the deceleration
To solve this problem, we can use the equations of motion for uniformly accelerated motion.
Let's start by finding the acceleration during the first 8 seconds when the particle is accelerating uniformly from rest.
We know the initial velocity (u) is 0 m/s, the final velocity (v) is 6 m/s, and the time (t) is 8 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, we can solve for the acceleration (a).
6 m/s = 0 m/s + a * 8 s
Rearranging the equation:
a = 6 m/s / 8 s
a = 0.75 m/s²
So, the acceleration during the first 8 seconds is 0.75 m/s².
Now, let's find the magnitude of the deceleration during the next 5 seconds when the particle decelerates uniformly to rest.
We know the initial velocity (u) is 6 m/s, the final velocity (v) is 0 m/s, and the time (t) is 5 s.
Using the same equation: v = u + at, we can solve for the deceleration (a).
0 m/s = 6 m/s + a * 5 s
Rearranging the equation:
a = (0 m/s - 6 m/s) / 5 s
a = -1.2 m/s²
So, the magnitude of the deceleration is 1.2 m/s².