Please explain this: The motion of an object moving at uniform acceleration can be described with the help of three equations, namely v = u + at s = ut + ½ at2 2as = v2 – u2 where u is the initial velocity of the object, which moves with uniform acceleration a for time t, v is its final velocity and s is the distance travelled in time t.
Answers
To derive : The equations ....
v = u + at
s = u + 1/2 at²
v² = u² + 2as
solution : let a particle moves with initial velocity u after time t, its velocity becomes v due to acceleration acting on particle is a.
see figure,
slope of velocity - time graph = acceleration
⇒(v - u)/(t - 0) = a
⇒v - u = at
⇒v = u + at .........(1)
area enclosed the velocity - time graph = displacement covered by particle
⇒area of trapezium formed as shown in figure = S
⇒S = 1/2 [v + u ] × t
from equation (1),
⇒S = 1/2 [u + at + u ] × t
⇒S = 1/2 [2u + at] × t
⇒S = ut + 1/2 at² ...........(2)
we know, acceleration, a = v dv/ds
⇒a ∫ds = ∫v dv
⇒a[s] = [v²/2]
⇒as = 1/2 [v² - u²]
⇒2as = v² - u²
⇒v² = u² + 2aS ............(3)
Answer:
Explanation:
The motion of an object moving at uniform acceleration can be described with the help of three equations, namely v = u + at s = ut + ½ at2 2as = v2 – u2 where u is the initial velocity of the object, which moves with uniform acceleration a for time t, v is its final velocity and s is the distance travelled in time t.