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

306.8264448 m

47.0016 m/s

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

Distance traveled by car

`s_c=ut+(1)/(2)at^2\\\Rightarrow s_c=(1)/(2)at^2`

Distance traveled by truck

`s_t=ut`

In order to overtake both distances should be equal

`(1)/(2)at^2=ut\\\Rightarrow (1)/(2)at=u\\\Rightarrow t=(2u)/(a)\\\Rightarrow t=(2* 23.5)/(3.6)\\\Rightarrow t=13.056\ s`

`s_c=(1)/(2)at^2\\\Rightarrow s_c=(1)/(2)3.6* 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=√(2as+u^2)\\\Rightarrow v=√(2* 3.6* 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