The position of an object moving along a line is given by $p(t) = 2t^3 - 2t +2$ . What is the speed of the object at $t = 4$ ?

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Answer 1 · 2017-12-18T13:27:21

$94ms^(-1)$

$p(t)=2t^3-2t+2$

to find the speed we differentiate

$p'(t)=6t^2-2$

for $t=2$

$p'(4)=6xx4^2-2$

speed $=94ms^(-1)$

SI units assumed

Answer 2 · 2017-12-18T13:30:22

The speed is $=94ms^-1$

The speed of an object is the derivative of the position.

$v(t)=(dp)/(dt)$

The position is

$p(t)=2t^3-2t+2$

The speed is

$v(t)=p'(t)=6t^2-2$

And when $t=4$

$v(4)=6*(4)^2-2=96-2=94ms^-1$

The position of an object moving along a line is given by p(t) = 2t^3 - 2t +2p(t) = 2t^3 - 2t +2. What is the speed of the object at t = 4 t = 4 ?