A test car with a dummy driver of mass 60 kg was propelled towards a rigid wall. If the speed of the dummy driver just before impact was 40m/s and the time between the collision and the dummy coming to the rest was 0.10 s, calculate: (i) the average retardation of the dummy driver during impact and (ii) the average force acting on the dummy driver due to the impact.

This will be solved like this

i part
A=v-u÷0.10
A=0-40÷0.10
A=-40÷0.10
A=-400m/s²
ii part
Force = mass × acceleration
F=60×400
F=24KN

To calculate the average retardation and the average force acting on the dummy driver due to the impact, we can use the kinematic equation:

v = u + at

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time

First, let's calculate the acceleration using the given information.

Given:
Initial velocity, u = 40 m/s
Final velocity, v = 0 m/s
Time, t = 0.10 s

Using the kinematic equation:

v = u + at
0 = 40 + a * 0.10

Rearranging the equation to solve for 'a':

a = (0 - 40) / 0.10
a = -400 m/s^2

(i) The average retardation of the dummy driver during impact is 400 m/s^2.

Next, let's calculate the average force acting on the dummy driver using Newton's second law of motion:

F = m * a

Where:
F = force
m = mass
a = acceleration

Given:
Mass of the dummy driver, m = 60 kg
Acceleration, a = -400 m/s^2

Substituting the values into the equation:

F = 60 kg * (-400 m/s^2)
F = -24,000 N

(ii) The average force acting on the dummy driver due to the impact is -24,000 N. The negative sign indicates that the force is being applied in the opposite direction of motion, in this case, stopping the dummy driver.

Note: The force is negative because it opposes the motion, which corresponds to the deceleration or retardation of the dummy driver.

To solve this problem, we need to use the equations of motion. Let's start with the first part:

(i) Average retardation of the dummy driver during impact.

We can use the formula:

v = u + at

where:
v = final velocity (0 m/s, since the dummy comes to rest)
u = initial velocity (40 m/s)
a = average acceleration/retardation (unknown)
t = time interval (0.10 s)

Rearranging the equation, we have:

a = (v - u) / t

Substituting the values we have:

a = (0 - 40) / 0.10
a = -400 m/s^2 (negative because it represents retardation)

Therefore, the average retardation of the dummy driver during impact is -400 m/s^2.

(ii) Average force acting on the dummy driver due to the impact.

To find the average force, we can use Newton's second law of motion:

F = ma

where:
F = force (unknown)
m = mass of the dummy driver (60 kg)
a = average acceleration/retardation (-400 m/s^2)

Substituting the values, we have:

F = 60 kg * (-400 m/s^2)
F = -24,000 N (negative because it represents an opposing force)

Therefore, the average force acting on the dummy driver due to the impact is -24,000 N.