A particle moves according to the law x - a cos- t -2- The distance covered by it in the time interval between t -0 to t -3 s isA- aB- 4 aC- 3 aD- 2 a

The correct option is C 3a Comparing the given equation with x = a cos ω t ω = π/2 or 2 π/T = π/2 ∴ T = 4s The given time t = 3 s is 3T/4 At time t = 0 partic ...

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Standard XII

Physics

Phase and the General Equation

A particle mo...

Question

A particle moves according to the law x = a cos $\frac{π t}{2} .$ The distance covered by it in the time interval between t = 0 to t = 3 s is

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Solution

The correct option is B
3a

Comparing the given equation with

$x = a c o s ω t$

$ω = \frac{π}{2}$

or $\frac{2 π}{T} = \frac{π}{2}$

$∴ T = 4 s$

The given time t = 3 s is $\frac{3 T}{4}$

At time t = 0 particle is at x = a (at extreme position) and at $t = 3 s = \frac{3 T}{4}$ it will be at mean position, x = 0

$∴$ distance covered will be 3a.

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A particle moves according to the law x = a cos πt2. The distance covered by it in the time interval between t = 0 to t = 3 s is

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