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

Answer 1

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.