A body starts from rest and accelerates to 2meter per second square for 6sec.it maintains this velocity for 10sec and then decelerates to rest in 4sec.calculate the acceleration
V = Vo + a*t = 0 + 2*6 = 12 m/s.
V = Vo + a*t.
0 = 12 + a*4, a = -3 m/s^2.
To calculate the acceleration, we need to find the change in velocity and the time taken for that change to occur in each of the three phases: acceleration, constant velocity, and deceleration.
In the first phase, the body starts from rest and accelerates to a velocity of 2 m/s^2 for 6 seconds. We can use the formula:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Since the initial velocity (u) is 0 m/s, the final velocity (v) is 2 m/s^2, and the time (t) is 6 seconds, we can rearrange the formula to find the acceleration (a):
a = (v - u) / t
Substituting the values:
a = (2 - 0) / 6
a = 2 / 6
a = 0.33 m/s^2
So, the acceleration during the first phase is 0.33 m/s^2.
During the second phase, the velocity remains constant at 2 m/s^2 for 10 seconds. Since there is no change in velocity, the acceleration is 0 m/s^2.
In the third phase, the body decelerates from 2 m/s^2 to rest in 4 seconds. The final velocity (v) is 0 m/s, the initial velocity (u) is 2 m/s^2, and the time (t) is 4 seconds. Using the same formula as before, we can find the acceleration:
a = (v - u) / t
a = (0 - 2) / 4
a = -2 / 4
a = -0.5 m/s^2
Note that the negative sign indicates deceleration.
So, the acceleration during the third phase is -0.5 m/s^2.
Therefore, the acceleration during the various phases are as follows:
- First phase: 0.33 m/s^2 (acceleration)
- Second phase: 0 m/s^2 (constant velocity)
- Third phase: -0.5 m/s^2 (deceleration)