Question

In a crash test, a car with a mass of 1600 kg is initially moving at a speed of 20 m/s just before it collides with a barrier. The final speed of the car after the collision is zero. The original length of the car is 4.50 m , but after the collision, the smashed car is only 3.60 m long.
Required:
a. What is the average speed Of the car during the period from first contact with the barrier to the moment the car comes to a stop? You may assume the force that the barrier exerts on the car is constant during this period.
b. How much time elapses between the moment the car makes first contact with the barrier and the moment it comes to a stop?
c. Making the very rough approximation that the large force that the barrier exerts on the car is approximately constant during contact, determine the approximate magnitude of this force?

Answer 1

Answer:

The answer to the given points can be defined as follows:

Explanation:

In point 1:

$\bold{v_f^2= v_i^2+2as}\\\\\to v_f=0\\\\\to v_i=20 \frac{m}{s}\\\\\to s= 4.50\ m -3.60 \ m$

      $=0.9 \ m$

put the value in the above formula:

$\to 0= 20^2+2 \times a \times 0.9\\\\\to -1.8\ a=400\\\\\to -a= \frac{400}{1.8} \\\\ \to a= -222.22\ \ \frac{m}{s^2}$

 $\bold{v_f=v_i+at}\\\\\to 0=20+ (-222.22)t\\\\\to 222.22t=20\\\\\to t=\frac{20}{222.22}\\\\\to t= 0.0900 \ s\\\\\to v_{avg}=\frac{s}{t}=\frac{0.9}{t}= 10\ \frac{m}{s}$

for point 2:

$t= 0.0900 \ s -\text{found above}$

for point 3:

$\to |a| = 222.22 \frac{m}{s^2} \text{found above}\\\\\to \bold{|F| = m \cdot |a|}$

         $=1600 \ kg \times 222.22 \ \frac{m}{s^2} \\\\= 3.55\times 10^{5} \ N$