a particle is moving with a velocity of 5m/s .after 5sec it is found to be moving with velocity of 12 m/s in a direction perpendicular to the original direction.during these 5sec find
1.change in speed,
2.change in velocity and magnitude of change in velocity ,
3.average acceleration and its magnitude .
1) change in speed: 12-5 = 7m/s
2) V1=5i & V2=12j
Change in vel.= V2-V1 = 12j-5i
its magnitude = sqrt(12^2+5^2)
= 13m/s^2
3) x-dir.: 0=5+Ax*5 => Ax= -1m/s^2
y-dir.: 12=0+Ay*5 => Ay= +12/5=2.4m/s^2
So A = -1i+2.4j
Mag. of av. acc.=sqrt(Ax^2+Ay^2)
To solve this problem, we need to calculate the change in speed, the change in velocity, magnitude of change in velocity, and average acceleration during the 5-second interval.
Given information:
Initial velocity (u) = 5 m/s
Final velocity (v) = 12 m/s
Time interval (t) = 5 seconds
1. Change in speed:
The change in speed is simply the difference between the final speed and the initial speed. It is given by the formula:
Change in speed = Final speed - Initial speed
Change in speed = v - u
Substituting the given values:
Change in speed = 12 m/s - 5 m/s = 7 m/s
Therefore, the change in speed is 7 m/s.
2. Change in velocity and magnitude of change in velocity:
The change in velocity is the difference between the final velocity vector and the initial velocity vector. Since the final velocity is perpendicular to the initial velocity, the change in velocity is equal to the magnitude of the final velocity vector.
Change in velocity = Final velocity
Change in velocity = v
Substituting the given value:
Change in velocity = 12 m/s
Therefore, the change in velocity is 12 m/s.
The magnitude of change in velocity can be found by taking the absolute value of change in velocity:
Magnitude of change in velocity = |Change in velocity|
Magnitude of change in velocity = |12 m/s|
Therefore, the magnitude of change in velocity is 12 m/s.
3. Average acceleration and its magnitude:
The average acceleration can be calculated using the formula:
Average acceleration = (Change in velocity) / Time interval
Average acceleration = Change in velocity / t
Substituting the given values:
Average acceleration = 12 m/s / 5 s = 2.4 m/s²
Therefore, the average acceleration is 2.4 m/s².
The magnitude of average acceleration can be found by taking the absolute value of average acceleration:
Magnitude of average acceleration = |Average acceleration|
Magnitude of average acceleration = |2.4 m/s²|
Therefore, the magnitude of average acceleration is 2.4 m/s².