Posted by Jennifer on .
Two cars approach each other from an initial distance of 2400 m. Car A is moving to the E at a constant rate speed of 40ms. Car B is moving to the W at a speed of 10ms but is accelarating at a rate of 2.00ms^2.
What is the time before the cars meet
the distance a traveled before meeting b
the relative speed at which the cars hit.
Call x = 0 the location were Car A starts. Call that car's location X1.
Car B then starts at x = 2400. Call its location X2
X1 = 40 t
X2 = 2400 - 10 t - t^2.
They meet when X1 = X2.
40t = 2400 -10 t - t^2
Rearrange that to read
t^2 +50 t -2400 = 0
(t +80)(t-30) = 0
Solve for the time t that is a positive root of that equation.
Use that value of t to solve for the location where they meet. The relative velocity is V1 - V2. But V2 is negative, so you end up adding the speeds of the cars at time t.