Question

displacement of a body is given by 3s=a+4bt*3 where a and b are constants. what is the velocity v at the end of 1 second.

Answer 1

Here, The position of the body is a function of time , i.e., x(t)= At + 4Bt³.

Now, velocity is defined as Rate of change of position of an object i.e., (position 2 - position 1 )/ (T2 - T1).

Derivative Also represents change in quantity. So in other words, *Velocity* Is Derivative of The Position of the object.

V(t) = A + 12Bt² ( using Power rule )

Power Rule- derivative of x^n = n.x^(n-1).

Acceleration is defined as *Rate of Change of Velocity*

So, the *Derivative of Velocity* gives *Acceleration*.

Therefore, acceleration here -

a(t) = 24Bt. ( Using Power rule again , Derivative of a constant is 0, therefore A is Vanished from here).

Hope this helps!


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