To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 28.0 km/hr approaches a car stopped at the red light. When the truck is 165.5 meters from the car the light turns green and the car immediately begins to accelerate at 2.4 m/s2. How close does the truck come to the car assuming the truck does not slow down?
How far from the stop light has the car travelled when the truck reaches its closest distance?

The easiest way through this is to use relativity. Relative motion makes it very easy, you'll see.

Consider that the truck is stationary (in other words, you are in the truck and you initially observe the car approaching towards you at 28 km/hr)

So, initial velocity of the car = - 28km/hr = 70/9 m/s
It has a constant acceleration of 2.4 m/s^2
The distance of separation is 165.5 m

So, use:

v^2 = u^2 + 2as

To find the distance travelled by the car until it's relative velocity becomes zero (ie when both the truck and the car are running at the same speed)

0 =(-\frac{70}{9})^2 + 2(2.4)s

We get s = 12.60 m

Hence, the car approached the truck by 12.60 m, making the closest distance = 165.5 - 12.6 = 152.9 m



For this part, don't use relative motion. Use v^2 = u^2 + 2as again.

When the car is closest to the truck, it's final velocity equals that of the truck. It started from rest, and you know the acceleration. Find s.

I have a question, we put (-)70/9, I mean the -.. because it said in the question "immediately begins to accelerate " ? Right?

Yes, but when using relative motion the speeds take a different aspect.

Let's say you're in the truck and you are going towards the car. The car is initially at rest. As you are in the truck, the car would initially appear as coming towards you at the same speed as you are approaching it, right? :)

I take forward as +ve and backwards as -ve here.