Question

a car is traveling on a straight road at 19 m/s. the driver sees a bird standing in the road 38 meters ahead and applies the brakes, giving constant deceleration of 5 m/s^2.

(a) how far away is the driver from the bird when he stops? ( assuming the bird doesn't move)

(b) how long does it take the driver to stop?

(c) the driver was in a 40 miles per hour zone. given that there are approximately 1.6 km in 1 mile, was the driver speeding?

Answer 1

Solution.

$v_0=19 m/s;$

$S_1=38m;$

$a=-5 m/s^2;$

$a) S_2=\dfrac{v^2-v_0^2}{2a};$

$S_2=\dfrac{-19^2}{-10}=36.1 m;$

$S=S_1-S_2; S=38-36.1=1.9m;$

$b) a=\dfrac{v-v_0}{t}\implies t=\dfrac{v-v_0}{a};$

$t=\dfrac{-19}{-5}=3.8s;$

$c)$ $v=40 mile /h;$

$1 mile=1.6 km;$

$19 m/s=68.4 km/h=42.75 mile/h;$

Answer: $a)S=1.9 m;$

$b) t=3.8s;$

$c)$ the driver exceeded the speed limit.