Question

In Fig. 2-27, a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x axis. At time t " 0, the red car is at xr " 0 and the green car is at xg " 220 m. If the red car has a constant velocity of 20 km/h, the cars pass each other at x " 44.5 m, and if it has a constant velocity of 40 km/h, they pass each other at x " 76.6 m. What are (a) the initial velocity and (b) the constant acceleration of the green car

Answer 1

 velocity, v_1v​1​​ be 20km/h20km/hwhich in m/sm/s is 5.55m/s5.55m/s. Let v_2v​2​​ be the 40km/h40km/h which is 11.1m/s11.1m/s.

To solve this problem, we will simultaneously solve two equations at once to find the initial velocity and the acceleration.

The two equations we will use are:

d-x_1=v_0t_1+\frac{1}{2}at_1^2d−x​1​​=v​0​​t​1​​+​2​​1​​at​1​2​​ where t_1=\frac{x_1}{v_1}t​1​​=​v​1​​​​x​1​​​​

and

d-x_2=v_0t_2+\frac{1}{2}at_2^2d−x​2​​=v​0​​t​2​​+​2​​1​​at​2​2​​ where t_2=\frac{x_2}{v_2}t​2​​=​v​2​​​​x​2​​​​

Subsisting x_1=44.5mx​1​​=44.5m and x_2=76.7mx​2​​=76.7m and our other given values leads us to the following results:

v_0=-13.9 m/sv​0​​=−13.9m/s and in km/h we have -50km/h.

and the acceleration is, a=-2.0m/s^2a=−2.0m/s​2​​.

As both values are negative, it tells us that it is along the -x direction.