Question

find instantaneous velocity at
t= pi/2 of a particle whose positional equation is given by
x(t) = 12cos²(t)​

Answer 1

satellite keeps moving in circular orbits .try finding out which category of inertia they are trying to maintain. a. Inertia of motion b. Inertia of rest c. Inertia of directionsatellite keeps moving in circular orbits .try finding out which category of inertia they are trying to maintain. a. Inertia of motion b. Inertia of rest c. Inertia of directionsatellite keeps moving in circular orbits .try finding out which category of inertia they are trying to maintain. a. Inertia of motion b. Inertia of rest c. Inertia of direction

Explanation:

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Answer 2

Concept:

• Differentiation
• Instantaneous velocity
• Velocity is displacement per unit time.

Given:

• t = π/2
• displacement x = 12cos²(t)​

Find:

• The instantaneous velocity v at t = π/2

Solution:

x = 12 cos²(t)​

v = dx/dt

We have to differential the positional equation with respect to t to obtain the velcity.

dx/dt = d12 cos²(t)​/dt

dx/dt = 12 d cos²(t)​/dt

dx/dt = 12 * 2 cos t * dcos(t)​/dt

dx/dt = 24 cos t * (-sin t)

dx/dt = -24 cos t sin t

dx/dt = -12 * 2cos t sin t

dx/dt = -12 sin 2t

v = -12 sin 2t

Instantaneous velocity at t = π/2

v (π/2) = -12 sin 2(π/2)

v (π/2) = -12 sin π

v (π/2) = -12*0

v (π/2) = 0

The instantaneous velocity is 0.

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