54. A car starting from rest and moving along a straight
path with uniform acceleration covers distances p
and q in the first two successive equal intervals of
time. Find the ratio of p to q.pearson foundation
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Answer:
p/q = 1/3
Explanation:
Given that car is starting from rest i.e u = 0
Consider the given time interval = t
Let the distance traveled in first interval of time is x₁
i.e p = x₁
Let the distance traveled in two time intervals is x₂
i.e q = x₂ - x₁.
Now, lets use the newtons second equation of motion.
i.e s = ut + 1/2 at²
=> x₁ = 0 + 1/2 at²
=> p = 1/2 at².
Then,
x₂ = 0 + 1/2 a(2t)²
=> x₂ = 4/2 at²
=> x₂ = 2 at²
so, q = x₂ - x₁
=> q = 2 at² - 1/2 at²
=> q = 3/2 at².
Now, p/q = (1/2 at²)/(3/2 at²)
=> p/q = 1/3
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