An object's two dimensional velocity is given by $v (t) = (5 t - t^{3}, 3 t^{2} - 2 t)$ $v(t) = ( 5t-t^3 , 3t^2-2t)$ . What is the object's rate and direction of acceleration at $t = 5$ $t=5$ ?

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Answer 1 · 2017-03-03T09:23:20

$a (5) = - 70 ˆ i + 28 ˆ j$ $a(5) = -70 hat i + 28 hat j$

$v (t) = 5 t - t^{3} ˆ i + 3 t^{2} - 2 t ˆ j$ $v (t) = 5t-t^3 hati + 3t^2-2t hatj$

$a (t) = \frac{d v}{d t}$ $a(t) = (dv)/dt$

$a (t) = 5 - 3 t^{2} ˆ i + 6 t - 2 ˆ j$ $a(t) = 5-3t^2 hat i + 6t-2 hat j$

$a (5) = 5 - 3 \times 5^{2} ˆ i + 6 \times 5 - 2 ˆ j$ $a(5) = 5-3xx5^2 hat i + 6xx5-2 hat j$

$a (5) = 5 - 75 ˆ i + 30 - 2 ˆ j$ $a(5) = 5-75 hat i + 30-2 hat j$

$a (5) = - 70 ˆ i + 28 ˆ j$ $a(5) = -70 hat i + 28 hat j$

Here, $ˆ i$ $hat i$ denotes $x$ $x$ direction and $ˆ j$ $hatj$ denotes $y$ $y$ direction.

An object's two dimensional velocity is given by v(t) = ( 5t-t^3 , 3t^2-2t)v(t)=(5t−t3,3t2−2t)v(t) = ( 5t-t^3 , 3t^2-2t). What is the object's rate and direction of acceleration at t=5 t=5t=5 ?