Question

If x denotes the displacement of an object in time ts and x = acos(πt) m, then acceleration of the object will be zero at​

Answer 1

Answer:

Acceleration

(a)= dt^2/d^2

= dt^2/d^2(a cost)

= −a dt/d(sin t)

=−a cost

Explanation:

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Answer 2

SOLUTION

GIVEN

x denotes the displacement of an object in time t s and x = a cos (πt) m

TO DETERMINE

The acceleration of the object will be zero at

EVALUATION

Here it is given that x denotes the displacement of an object in time t s

$\displaystyle \sf{ x = a \: \cos (\pi t)}$

Differentiating both sides with respect to t we get

$\displaystyle \sf{ Velocity = v = \frac{dx}{dt} = - a \pi\: \sin (\pi t)}$

Again Differentiating both sides with respect to t we get

$\displaystyle \sf{ Acceleration = f = \frac{dv}{dt} = - a {\pi}^{2} \cos (\pi t)}$

Now acceleration = 0

$\displaystyle \sf{ \implies \frac{dv}{dt} = 0}$

$\displaystyle \sf{ \implies - a {\pi}^{2} \cos (\pi t)} = 0$

$\displaystyle \sf{ \implies \cos (\pi t)} = 0$

$\displaystyle \sf{ \implies \pi t = (2n + 1) \frac{\pi}{2} }$

$\displaystyle \sf{ \implies t = \frac{2n + 1}{2} }$

$\displaystyle \sf{ \implies t = n + \frac{1}{2} }$

Where n is a whole number

FINAL ANSWER

Acceleration will be zero when

$\displaystyle \sf{ t = n + \frac{1}{2} }$

Where n is a whole number

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