Question

When a driver presses the brake pedal, his car can stop with an acceleration of 5.4 m/s2. How far will the car travel while coming to a complete stop if its initial speed was 25 m/s?
A.25.1 m
B.2.31 m
C.57.9 m
 D.101.4 m

Answer 1

$Given:\\a=5.4 \frac{m}{s^2} \\v_0= 25\frac{m}{s} \\\\Find:\\s=?\\\\Solution:\\\\s=v_0t- \frac{at^2}{2} \\\\a= \frac{\Delta v}{t} \\\\v_e=0\Rightarrow \Delta v=v_0\\\\t= \frac{v_0}{a} \\\\s= \frac{v_0^2}{a} - \frac{v_0^2}{2a} =\frac{v_0^2}{2a} \\\\s= \frac{ (25\frac{m}{s})2 }{2\cdot 5.4 \frac{m}{s^2} } \approx 57.9m\\\\C\rightarrow Correct\;answer$