A car, of total mass 1200 kg, is travelling at 90 km/h and strikes a tree. The front end of the car compresses and the driver comes to rest after travelling 0.80 m.

(i)What was the average acceleration of the driver during the collision? Express the answer in terms of “g’s”.
(4 %)
(ii)How much energy was dissipated in the collision?

i) Is 4% your guess at the answer?

If a is the deceleration rate,
Vinitial = sqrt(2 a X)
Solve for a. Convert Vinitial to m/s first.
ii) ALL of the initial kinetic energy was dissipated.

To answer these questions, we need to use the principles of physics and some equations related to acceleration and energy.

(i) To find the average acceleration of the driver during the collision, we can use the formula for average acceleration:

Average acceleration = Change in velocity / Time taken

First, we need to find the change in velocity. Given that the car comes to rest, the initial velocity can be calculated by converting 90 km/h to m/s:

Initial velocity (v1) = 90 km/h = 90 * (1000 m / 3600 s) = 25 m/s

The final velocity (v2) is 0 m/s because the car comes to rest.

Using the formula for change in velocity, we can calculate:

Change in velocity (Δv) = v2 - v1 = 0 m/s - 25 m/s = -25 m/s

We also need to find the time taken (t) during the collision. We can use the equation of motion for distance with constant acceleration:

Distance = Initial velocity * time + 0.5 * acceleration * time^2

In this case, the distance is given as 0.80 m, the initial velocity is 25 m/s, and the final velocity is 0 m/s. Assuming the car decelerates uniformly, the equation becomes:

0.80 = 25 * t + 0.5 * acceleration * t^2

Simplifying the equation, we can rewrite it as:

0.5 * acceleration * t^2 + 25 * t - 0.80 = 0

Now we can solve this quadratic equation to find the value of time (t). Once we have the value of t, we can use it to calculate the average acceleration.

(ii) To find the energy dissipated in the collision, we can use the principle of conservation of mechanical energy. The energy dissipated is equal to the kinetic energy of the car before the collision minus the kinetic energy of the car after the collision:

Energy dissipated = 0.5 * mass * (v1)^2 - 0.5 * mass * (v2)^2,

where mass is the total mass of the car (given as 1200 kg), v1 is the initial velocity, and v2 is the final velocity.

Plugging in the values, we can calculate the energy dissipated in the collision.

By following these steps, we can find the average acceleration of the driver during the collision and the amount of energy dissipated.