A car traveling at 26.8 m/s hits a stone wall . The driver, who is wearing a shoulder harness and seat belt, moves forward 0.99 m as the car stops. Assuming his acceleration is uniform, find his acceleration. in m/s2? (don't forget the (-) if negative)
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To find the acceleration of the car, we can use the following formula:
acceleration = Δv / Δt
Where:
Δv = change in velocity
Δt = change in time
Given that the car stops, we know that the final velocity (vf) is 0 m/s, and the initial velocity (vi) is 26.8 m/s.
Δv = vf - vi = 0 - 26.8 = -26.8 m/s
Next, we need to find the time it takes for the car to come to a stop. We can use the following formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since we want to find the acceleration, we'll rearrange the equation to solve for time:
(time^2 * 0.5 * acceleration) + (initial velocity * time) - distance = 0
Using the quadratic formula, we can solve for time. However, we already know the values for distance and initial velocity:
distance = 0.99 m (driver's forward displacement)
initial velocity = 26.8 m/s
Substituting the known values into the equation:
(time^2 * 0.5 * acceleration) + (26.8 * time) - 0.99 = 0
Solving this quadratic equation, we find the value of time. Since the driver moves forward, we only need the positive value for time. Let's denote that as t.
Now that we have the value of Δv and t, we can calculate the acceleration:
acceleration = Δv / Δt
Substituting the values:
acceleration = (-26.8 m/s) / t
Solving for acceleration will give us the answer.
Note: To accurately solve the quadratic equation, we need the value of t. However, it is not provided in the question. Please double-check if all the necessary information has been given, or if there is any additional information that can be used to find the value of time.