Minimum Deceleration for Car to Avoid Truck: Physics Homework

[TeeNaa]

Homework Statement

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?

Homework Equations

I know acceleration is a = (Vf - vi)/t but I do not know how to get the acceleration/deceleration when there two object instead of just let a car moving.

The Attempt at a Solution

I know the Vi of the Car is = 27.8 m/s
The Vf of the Car is 13.9 m/s (The acceleration of the truck is this so won't it be the final velocity of the car when it crash?)
Distance of car travel = 200+x
Distance of truck travel = x;

Can someone guide me in the right direction? Thanks

 

[STEMucator]

Homework Statement

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?

Homework Equations

I know acceleration is a = (Vf - vi)/t but I do not know how to get the acceleration/deceleration when there two object instead of just let a car moving.

The Attempt at a Solution

I know the Vi of the Car is = 27.8 m/s
The Vf of the Car is 13.9 m/s (The acceleration of the truck is this so won't it be the final velocity of the car when it crash?)
Distance of car travel = 200+x
Distance of truck travel = x;

Can someone guide me in the right direction? Thanks

Notice that the distance between the car and truck is decreasing at a rate of 100km/h - 50km/h = 50km/h.

Also note that 200m = 0.2km. These will help you find time.

Using this you can determine the proper acceleration.

 

[TeeNaa]

I understand when you say the decrease in the distance due to the different in the vehicle speed but I can't think of how to find the time when the truck and car is constantly moving. Thank you

 

[STEMucator]

I understand when you say the decrease in the distance due to the different in the vehicle speed but I can't think of how to find the time when the truck and car is constantly moving. Thank you

Remember that when you're dealing with speed :

$$v = \frac{Δd}{Δt}$$

So that :

$$Δt = \frac{Δd}{v}$$

 

[CAF123]

I understand when you say the decrease in the distance due to the different in the vehicle speed but I can't think of how to find the time when the truck and car is constantly moving. Thank you

Put one car at an origin. Write its displacement as a function of time. Put the truck 200m along the x-axis and then write its displacement as a function of time. Equate these to find the time to collision as a function of acceleration.

 

[TeeNaa]

Thank you for the replies guy.
I came up with that since the truck will travel a certain distance before the car hit, the distance for the can can be dCar = 200m + x . Since x is the distance the truck travel, it can be represented as x = ((Vf + Vi)/2) * t - 200.
since x = distance, x can be x = vt (velocity * time). Is this how to approach this problem without using relative velocity? I'm stuck after this part.