The position of an object moving along a line is given by $p(t) = 2t - sin(( pi )/3t)$ . What is the speed of the object at $t = 8$ ?

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Answer 1 · 2018-07-20T01:13:02

The speed of the object at $t=8$ is approximately $s=120.8 m/s$

I will be rounding to the nearest decimal place for convenience

Speed is equal to distance multiplied by time, $s=dt$

First, you want to find the position of the object at $t=8$ by plugging in $8$ for $t$ in the given equation and solve

$p(8)=2(8)-sin((8pi)/3)$
$p(8)=16-sqrt3/2$

$p(8)=15.1$

Assuming that $t$ is measured in seconds and distance ( $d$ )is measured in meters, plug into the speed formula

$s=dt$

$s=15.1m*8s$

$s=120.8 m/s$

The position of an object moving along a line is given by p(t) = 2t - sin(( pi )/3t) p(t) = 2t - sin(( pi )/3t) . What is the speed of the object at t = 8 t = 8 ?