Acceleration and time taken by a car to increase speed (8329)

, por F_y_Q

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A car, which has uniformly accelerated motion, increases its speed from 18 km/h to 72 km/h over a straight distance of 37.5 meters. Calculate the time taken for this journey and its acceleration.

P.-S.

To make the problem homogeneous, the first step is to express the speeds in SI units:

\left 18\ \dfrac{\cancel{km}}{\cancel{h}}\cdot \dfrac{10^3\ m}{1\ \cancel{km}}\cdot \dfrac{1\ \cancel{h}}{3.6\cdot 10^3\ s} = {\color[RGB]{0,112,192}{\bm{5\ m\cdot s^{-1}}}} \atop 72\ \dfrac{\cancel{km}}{\cancel{h}}\cdot \dfrac{10^3\ m}{1\ \cancel{km}}\cdot \dfrac{1\ \cancel{h}}{3.6\cdot 10^3\ s} = {\color[RGB]{0,112,192}{\bm{20\ m\cdot s^{-1}}}} \right \}

You can relate the change in speed and the distance covered with the car’s acceleration:

v_f^2 = v_i^2 + 2ad\ \to\ \color[RGB]{2,112,20}{\bm{a = \frac{(v_f^2 - v_i^2)}{2d}}}

Substitute the values and calculate:

a = \frac{(20^2 - 5^2)\ m\cancel{^2}\cdot s^{-2}}{2\cdot 37.5\ \cancel{m}} = \fbox{\color[RGB]{192,0,0}{\bm{5\ m\cdot s^{-2}}}}


The time needed to make this speed change is:

v_f = v_i + a\cdot t\ \to\ \color[RGB]{2,112,20}{\bm{t = \frac{v_f - v_i}{a}}}

Substitute and calculate:

t = \frac{(20 - 5)\ \cancel{m}\cdot \cancel{s^{-1}}}{5\ m\cdot s^{\cancel{-2}}} = \fbox{\color[RGB]{192,0,0}{\bf 3\ s}}