Question

A particle is moving with displacement x=4t^4 + 3t^3 +2t^2 + 6t + 4. Find the velocity of the object when time is 1 second

Answer 1

velocity

• slope of displacement-time with t-axis.
• differentiation of displacement with respect to time.
• total displacement covered in time taken.

$\implies \rm v = \dfrac{dx}{dt}$

$\implies \rm v = \dfrac{d(4t^4 +3t^3+2t^2+6t +4)}{dt}$

$\implies \rm v = 16t^3 +9t^2+4t+6+0$

Now, velocity at t=1s,

$\implies \rm v = 16(1)^3 +9(1)^2+4(1)+6$

$\implies \rm v = 16 +9+4+6$

$\implies \rm v = 35\: ms^{-1}$

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