A particle accelerates from rest at a constant rate for some time and attains a velocity of 8 meter per second. Afterwards it decelerates with the consent rate and comes to rest. If the total time taken is 4 second then what is the total distance covered by the particle?
average speed-4m/s
distance= avgspeed*time=4m/s*4s=16m
To find the total distance covered by the particle, we need to break down the motion of the particle into two parts: the acceleration phase and the deceleration phase.
In the acceleration phase:
1. The initial velocity (u) is 0 m/s (particle is at rest).
2. The final velocity (v) is 8 m/s.
3. The time taken (t) is given as 4 seconds.
Using the formula for acceleration:
v = u + at
Here, v = 8 m/s, u = 0 m/s, and t = 4 seconds. We can rearrange the formula to solve for acceleration (a):
a = (v - u) / t
a = (8 - 0) / 4
a = 2 m/s^2
Now, we can calculate the distance covered during the acceleration phase using the equation:
s = ut + (1/2)at^2
Here, s represents the distance covered during the acceleration phase. Let's plug in the values:
s = 0(4) + (1/2)(2)(4^2)
s = 0 + (1/2)(2)(16)
s = 0 + (1/2)(32)
s = 0 + 16
s = 16 meters
Therefore, during the acceleration phase, the particle covers a distance of 16 meters.
In the deceleration phase, the particle comes to rest, so the final velocity (v) is 0 m/s. The initial velocity (u) is 8 m/s, and we can still use the acceleration (a) value of 2 m/s^2.
Using the formula:
v = u + at
0 = 8 + 2t
-8 = 2t
t = -4 seconds
Since time cannot be negative, we can infer that the deceleration phase takes 4 seconds.
Now, we can calculate the distance covered during the deceleration phase using the same equation:
s = ut + (1/2)at^2
Let's plug in the values:
s = 8(4) + (1/2)(2)(4^2)
s = 32 + (1/2)(2)(16)
s = 32 + (1/2)(32)
s = 32 + 16
s = 48 meters
Therefore, during the deceleration phase, the particle covers a distance of 48 meters.
To find the total distance covered, we need to add the distances covered during both phases:
Total distance = acceleration distance + deceleration distance
Total distance = 16 meters + 48 meters
Total distance = 64 meters
Hence, the total distance covered by the particle is 64 meters.