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nephleonidas · Aug 23, 2010, 07:52 PM

A cab driver picks up a customer and delivers her 3.50 km away, driving a straight route. The driver accelerates to the speed limit and, upon reaching it, begins to decelerate immediately. The magnitude of the deceleration two times the magnitude of the acceleration. Find the lengths of the acceleration and deceleration phases of the trip in km

Clough · Aug 23, 2010, 11:40 PM

Originally Posted by nephleonidas

A cab driver picks up a customer and delivers her 3.50 km away, driving a straight route. The driver accelerates to the speed limit and, upon reacing it, begins to decelerate immediately. The magnitude of the deceleration two times the magnitude of the acceleration. Find the lengths of the acceleration and deceleration phases of the trip in km

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ebaines · Aug 24, 2010, 07:24 AM

Here's a hint: use the formula:
$<br /> v_f^2 - v_i^2 = 2 a_1 d_1$ .

For the first phase $v_i =0$ , and for the second phase the initial velocity is equal to the final velocity of the first phase - that's the peak velocity, which we can call $v_{max}$ , while the final velocity is 0. So:

$<br /> v_{max}^2 = 2 a_1 d_1 = 2a_2 d_2<br />$

You know that $a_2 = 2 \times a_1$ , and that $d_1 + d_2 = 3.5$ Km. So you now have three equations in three unknowns ( $a_1, d_1$ and $d_2$ ). Can you take it from here?