Question

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead (from rest) with a constant acceleration of 2.9 m/s². At the same instant, a truck traveling with a constant speed of 36.3 mph passes the car. How much time in seconds does it take the car to catch up with the truck. Keep 2 decimal places.

Answer 1

It take the car to catch up with the truck 111.91 s.

Step-by-step explanation:

To solve this problem we have to use the formula for uniformly accelerated motion (for the car) and the formula for uniform rectilinear movement (for the truck).

We apply the corresponding formula for each vehicle, so we will have two equations. As the question is how much time, time is the unknown variable that we will call t from now on.

Equation for the car is:

`x_(c)=(1)/(2)*a*t^(2)`

Equation for the truck is

`x_(t) =v*t`

We know that t will be the same for the two vehicle on the instant the car catch up the truck.

On the time t the distance x traveled for both cars are the same, so we can equate the two formulas ans isolate t.

`v*t=(1)/(2) *a*t^(2) \\t=(2*v)/a\\t=111,91s`

Note: all unit of measurement must be the same, for speed, we need to convert 36,3mph to m/s.

36,3mph=162.27m/s we use 162.27m/s in the formulas.