How Long Will It Take for the Car to Collide with the Truck?

[wangwang2626]

Ok so the car is 25 m behind a truck which suddenly braked. I put it as decelerating at -6.5 m/s it was traveling at 110km/h . I would like to know how long it takes to collide with the truck , and if it dosent what would I have to change the deceleration to be so that it does collide with the truck?
What I did was
v=vo+at
t=(v-vo)/a
t=30.5556/(-6.5)
but that's obviously wrong
I don't know what to do next
or what other formula to use

 

[rude man]

How fast was the car going and how fast is it decelerating, starting with how long after the truck is decelerating?

 

[wangwang2626]

the car was traveling at 110km/h when they noticed that the truck was not moving , it was 25 meters behind , I said it was decelerating at 6.5 m/s so how long would it take till it got to the truck and at what speed would it hit the truck. If the car does not reach the truck can you please suggest a different deceleration?

 

[rude man]

In the absence of the truck, how much distance is covered by the car from the moment it starts to decelerate until its speed = 0? Is that distance < or > 25m? (Hint: you first need to compute the time to decelerate to zero, which you have already done except for the wrong sign).

When you get this part we can continue with the second part of the question.

 

[Nickie]

To calculate the time it takes for the car to collide with the truck, you can use the formula for distance, d = v0t + 1/2at^2, where d is the distance, v0 is the initial velocity, a is the deceleration, and t is the time. In this case, the initial velocity is 110 km/h, which is equivalent to 30.5556 m/s. The distance is 25 m, and the deceleration is -6.5 m/s^2. Plugging these values into the formula, we get:

25 = 30.5556t + 1/2(-6.5)t^2

Solving for t, we get t = 2.75 seconds. This means that it will take 2.75 seconds for the car to collide with the truck.

If you want to change the deceleration so that the car collides with the truck, you can rearrange the formula to solve for a:

a = (d - v0t) / (1/2t^2)

Substituting the values, we get:

a = (25 - 30.5556*2.75) / (1/2*2.75^2) = -14.6 m/s^2

So, in order for the car to collide with the truck, the deceleration needs to be increased to -14.6 m/s^2. Keep in mind that this calculation assumes that the truck remains at a constant distance of 25 m from the car. If the truck moves or the car swerves, the collision time will be different.