Question

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 truck’s rear end? (This is called the "​minimum trailing distance​".) 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!))

Answer 1

To solve this problem, we need to make the assumption that the braking acceleration of the car and the truck are the same. The minimum trailing distance between the car and the truck can be found using the expression d = (v^2)/(2a).

Step-by-step explanation:

In order to solve this problem, we need to make the assumption that the braking acceleration of the car and the truck are the same. This assumption simplifies the calculations.

To find the minimum trailing distance, we can analyze the motion of both the car and the truck. Since both vehicles have the same braking acceleration, the velocity-time graph for both car and truck would show a linear decrease in velocity. The acceleration-time graph would show a constant negative acceleration.

The expression for the minimum trailing distance can be derived using the equations of motion. Let's denote the initial velocity of both car and truck as v, and the acceleration as a. The minimum trailing distance can be expressed as d = (v^2)/(2a).

To find the numerical value for the minimum trailing distance, we would need to know the specific values of the initial velocity and acceleration for both car and truck.

Answer 2

Step-by-step explanation:

Let the velocity of car and truck be u and breaking acceleration be a .

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