You are driving a car behind a truck. Both your car and the truck are moving at a speed of 80km/hr. If the driver of the truck suddenly slams on the brakes, what minimum distance betweenyour car and the truck is needed so that your car does not crash into the truckâ€™s rear end? (This is called the "â€‹minimum trailing distanceâ€‹".) To simplify this problem, assume that the truck andthe car have the same braking acceleration.

a. In order to simplify the calculations for this problem, you are told to assume that the braking acceleration of the car and the truck are the same. What other reasonable assumptions do you need to make in order to solve this problem?
b. For both the truck and the car, draw an acceleration- and velocity-versus-time graph.
c. Find an expression for the minimum trailing distance. (Your expression should only contain symbols of physical quantities. No numbers are needed here.)
d. Find the numerical value for the minimum trailing distance (Plug the values of physical quantities into your expression from part A (do not forget units!))

We shall have to assume the reflex time of the driver of the car . By the time he applies brake , his car will cover some distance . There will be some time tag between the time the truck starts decelerating and the driver of the car responding to that . During this period the car will not start decelerating . It will keep on moving with uniform velocity of u .

Let this time lag be t .

b )

For answer see the attached file

c )

The minimum trailing distance will be the distance covered by car before it starts decelerating in response to truck's deceleration .

minimum trailing distance d = u x t

d ) u = 80 km / h = 22.22 m /s

reflex action time t = 0.1 s ( assumed time )

d = 22.22 x .1

= 2.2 m