Question

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.60 m/s^2 . At the same instant a truck, traveling with a constant speed of 23.5 m/s , overtakes and passes the car. a. How far beyond its starting point does the car overtake the truck?b. How fast is the car traveling when it overtakes the truck?

Answer 1

Answer:

306.8264448 m

47.0016 m/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

Distance traveled by car

$s_c=ut+\dfrac{1}{2}at^2\\\Rightarrow s_c=\dfrac{1}{2}at^2$

Distance traveled by truck

$s_t=ut$

In order to overtake both distances should be equal

$\dfrac{1}{2}at^2=ut\\\Rightarrow \dfrac{1}{2}at=u\\\Rightarrow t=\dfrac{2u}{a}\\\Rightarrow t=\dfrac{2\times 23.5}{3.6}\\\Rightarrow t=13.056\ s$

$s_c=\dfrac{1}{2}at^2\\\Rightarrow s_c=\dfrac{1}{2}3.6\times 13.056^2\\\Rightarrow s_c=306.8264448\ m$

The distance the car has to travel is 306.8264448 m

$v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 3.6\times 306.8264448+0^2}\\\Rightarrow v=47.0016\ m/s$

The speed of the car when it overtakes the truck is 47.0016 m/s