(a) Derive a relation between initial velocity 'u', final velocity v and distances covered by a body moving with uniform acceleration 'a'.
(b) A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 5 m/ s2 for 10s. Find the distance covered by motor boat in this time.
CBSE Class IX Science LA (5 Marks)
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Answered by
1
v×v - u×u=2 as
s= 250m
s= 250m
Answered by
1
(a) The first equation of motion is v = u + at
v – u = at ....(1)
Average velocity = s / t ...(2)
Average velocity = u + v / 2 --(3)
From equation (2) and equation (3) we get,
u + v / 2 = s / t ......(4)
Multiplying equation (1) and equation (4) we get,
(v – u) (v + u) = at x 2s / t
(v – u) (v + u) = 2as [a² - b² = (a + b) (a – b)] v²- u² = 2as (III equation of motion)
(b) s = ut + 1/2 at²
= 0 x t + 1/2 x 5 x 10 x 10
= 1/2 x 5 x 100
= 5 x 50
= 250 m.
v – u = at ....(1)
Average velocity = s / t ...(2)
Average velocity = u + v / 2 --(3)
From equation (2) and equation (3) we get,
u + v / 2 = s / t ......(4)
Multiplying equation (1) and equation (4) we get,
(v – u) (v + u) = at x 2s / t
(v – u) (v + u) = 2as [a² - b² = (a + b) (a – b)] v²- u² = 2as (III equation of motion)
(b) s = ut + 1/2 at²
= 0 x t + 1/2 x 5 x 10 x 10
= 1/2 x 5 x 100
= 5 x 50
= 250 m.
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