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

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

Hi, nephleonidas!

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Thanks!

Here's a hint: use the formula:

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:


v_{max}^2 = 2 a_1 d_1 = 2a_2 d_2


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?