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PhysicsQ&A LibraryA particle moves along the +ve direction of x-axis. Its position x depends on time t as x=at3+bt2+c+d. Let dx/dt represent instantaneous velocity d2x/dt2 represents instantaneous acceleration (α) of the particle.The average acc. of the particle is defined as <α> =∫αdt/dt. Find the average acc. in time interval t=0 to t=1s.Question

Asked Jan 16, 2020

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A particle moves along the +ve direction of x-axis. Its position x depends on time t as x=at^{3}+bt^{2}+c+d. Let dx/dt represent instantaneous velocity d^{2}x/dt^{2} represents instantaneous acceleration (**α**) of the particle.The average acc. of the particle is defined as <**α**> =∫αdt/dt. Find the average acc. in time interval t=0 to t=1s.

Step 1

Given:

Position of particle (x)=at^{3}+bt^{2}+c+d

Step 2

differentiating w.r.t t to get instantaneous velocity.

Step 3

Differentiating w.r.t t to get instan...

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