A car traveling 100 km/h is 200m away from a truck traveling 50 km/h (in the same direction). Assuming constant braking acceleration, what is the minimum deceleration the car must have if it is not to hit the truck?

Can someone hint me on how I can start this problem? Thanks

Car Speed=100km/h=100000m/3600s=27.8m/s

Truck Speed =(50/100) * 27.8=13.9 m/s.

V^2 = Vo^2 + 2a*d
a = (V^2-Vo^2)/2d
a = (0-(27.8-13.9)^2)/400 = -0.483 m/s^2

NOTE: The effective speed of the car is less than the actual speed, because the truck is moving forward.

Correction: The speed of the car does not have to be reduced to zero, because

the truck is moving forward. It must be reduced to 50 km/h(13.9m/s).

a = (V^2-Vo^2)/2d
a = (13.9^2-27.8^2)/400 = -1.45 m/s^2.

To solve this problem, we can use the concept of relative velocity.

First, let's determine the relative velocity between the car and the truck. The relative velocity is equal to the difference between the velocities of the car and the truck, given that they are traveling in the same direction.

Relative velocity (v_rel) = Velocity of the car - Velocity of the truck

Therefore, v_rel = 100 km/h - 50 km/h = 50 km/h

Now, we need to convert the relative velocity into meters per second (m/s). We know that 1 km/h is equal to 0.2778 m/s.

So, v_rel = 50 km/h * 0.2778 m/s/km = 13.89 m/s

Since the car is 200 meters away from the truck, we can use the equation of motion to determine the minimum deceleration required by the car. The equation of motion is:

v_final^2 = v_initial^2 + 2 * a * d

where v_final is the final velocity (0 m/s in this case as the car needs to stop), v_initial is the initial velocity (13.89 m/s), a is the deceleration we need to find, and d is the distance between the car and the truck (200 m).

Substituting the values into the equation, we get:

0^2 = (13.89 m/s)^2 + 2 * a * 200 m

0 = 193.21 m^2/s^2 + 400 a

Simplifying the equation:

400 a = -193.21 m^2/s^2

Finally, solving for a, the minimum deceleration required by the car:

a = -0.483 m/s^2

Therefore, the minimum deceleration the car must have to avoid hitting the truck is approximately 0.483 m/s^2 in the opposite direction of its motion.