In the figure here, a red car and a green car move toward each other in adjacent

Question

In the figure here, a red car and a green car 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 = 212 m. If the red car has a constant velocity of 26.0 km/h, the cars pass each other at x = 43.8 m. On the other hand, if the red car has a constant velocity of 52.0 km/h, they pass each other at x = 76.5 m. What are (a) the initial velocity (in km/h) and (b) the (constant) acceleration (in m/s2) of the green car? Include the signs.

Explanation / Answer

Since they are passing each other, they are moving towards each other

velocity of the red car = 26km/h = 7.22 m/s
time taken by the red car to reach the point where the red car and the green car pass each other = 43.8/7.22 = 6.08s
distance traveled by the green car = 212-43.8 = 168.2m

when the red car has velocity 52km/hr = 14.44m/s
time taken by the red car to reach the point where the red car and the green car pass each other = 76.5/14.44 = 5.31s
distance traveled by the green car = 212-76.5 = 135.5m

In the first case , for the green car,

using s(distance) = u[initial velocity] X t[time] + a[acceleration] X t2/2

we get, 168.2 = 6.08u + 18.48a

u = [168.2 - 18.48a]/6.08

In the second case.

135.5 = 5.31u + 14.1a

taking the value of u from the first equation,

we get the value of a as 5.84m/s2

putting the value of a in u = [168.2 - 18.48a]/6.08, we get u = 10 m/s

Also, u would be negatiove since the green car has to travel in the negative direction.

a will have positive sign

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