A car is proceeding at a speed of 14.0 m/s when it collides with a stationary car in front. During the collision, the fist car moves a distance of 0.350 m as it comes to a stop. The driver is wearing her seat belt, so she remains in her seat during the collision. The driver’s mass is 60.0 kg. Neglect any friction between the driver and the seat.

To find the deceleration (or acceleration) of the car during the collision, we can use the equation:

acceleration = (final velocity - initial velocity) / time

Since the car comes to a stop during the collision, the final velocity is 0 m/s. The initial velocity is given as 14.0 m/s. We need to find the time it takes for the car to come to a stop.

We can use the equation of motion:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

Plugging in the known values, we have:

0.350 m = (14.0 m/s * time) + (0.5 * acceleration * time^2)

Now, we can solve this equation to find the time.

First, let's multiply both sides of the equation by 2 to remove the factor of 0.5:

0.70 m = 28.0 m/s * time + acceleration * time^2

Next, rearrange the equation:

acceleration * time^2 + 28.0 m/s * time - 0.70 m = 0

This is a quadratic equation in terms of time. We can use the quadratic formula to solve for time:

time = (-b ± √(b^2 - 4ac)) / 2a

For this equation, a = acceleration, b = 28.0 m/s, and c = -0.70 m.

Substituting these values into the formula, we get:

time = (-(28.0 m/s) ± √((28.0 m/s)^2 - 4 * acceleration * (-0.70 m))) / (2 * acceleration)

Now, we need to find the value of acceleration.

Using the first equation mentioned in the beginning (acceleration = (final velocity - initial velocity) / time), and plugging in the values of final velocity, initial velocity, and time, we can solve for acceleration:

acceleration = (0 m/s - 14.0 m/s) / time

Substituting this into the equation for time, we now have:

time = (-(28.0 m/s) ± √((28.0 m/s)^2 - 4 * ((0 m/s - 14.0 m/s) / time) * (-0.70 m))) / (2 * ((0 m/s - 14.0 m/s) / time))

Simplifying this equation, we get:

time = (-(28.0 m/s) ± √((28.0 m/s)^2 + 4 * 14.0 m/s * (-0.70 m))) / (2 * 14.0 m/s / time)

Finally, we can solve for time by choosing the appropriate sign (positive or negative) in the quadratic formula. Once we have the value of time, we can substitute it back into the equation for acceleration:

acceleration = (0 m/s - 14.0 m/s) / time

This will give us the deceleration (or acceleration) of the car during the collision.