Question

A bus passes by a car which is at rest. When the bus is 200 m ahead of the car, the bus having a velocity of 108 kph at that point, decelerates at 0.50m/s^2. One second later, the car moves and accelerates at 4mps^2. When and where will the car overtake the bus?

Please help.. :)

Answer 1

Let t be the time at which the car has traveled the same distance as the bus.
We can make use of the displacement equation:
\[\large x=v _{0}t+\frac{1}{2}at ^{2}\]
\[\large d _{bus}=200+30(t+1)-\frac{0.5}{2}(t+1)^{2}\ .........(1)\]
\[\large d _{car}=\frac{4t ^{2}}{2}\ ..............(2)\]
Equating the distances traveled by the bus and the car results in the following quadratic equation:
\[\large 2.25t ^{2}-29.5t-229.75=0\]
The real solution to this quadratic is t = 18.6 seconds.
The distance traveled can be found by substitution in equation (2).