Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1 000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.40 m above the floor. If the floor is hardwood, the child’s head is brought to rest in approximately 2.0 mm. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume that the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate.

A boxer's fist and glove have a mass of m = 1.04 kg. The boxer's fist can obtain a speed of v = 9.25 m/s in a time of t = 0.21 s. Write a symbolic expression for the magnitude of the average acceleration, aave, of the boxer's fist, in terms of the variables provided.  Find the magnitude of the average acceleration, aave, in meters per square second. Write an expression for the magnitude of the average net force, Fb, that the boxer must apply to his fist to achieve the given velocity. (Write the expression in terms of m, v and t.) What is the numerical value of Fb, in newtons?

A car is moving at 18.00[m/s], and comes to a stop in 3.45[s], due to friction acting on the car. Assuming the acceleration is constant, what is the magnitude of the acceleration experienced by the car? Express your answer in m/s2.

Elon Musk’s SpaceX is proposing that commercial flights will be ready to go to the Moon in less than three years. Yusaku Maezawa, a Japanese billionaire, is seeking eight artists to join his trip to the Moon. He wants them to inspire everyone by creating artwork after they return to Earth. The acceleration due to gravity on the surface of the Moon is 16.6% of the acceleration due to gravity on Earth. To keep the artists comfortable, it is decided that as they lift off from the Moon, the acceleration they experience close to the surface of the Moon should be kept to the equivalent of 2.83 g (1?is the acceleration due to gravity on the surface of the Earth). What is the maximum thrust that one of the new rockets from Part 2 can withstand under this condition? Note: The weight of the artists is negligible compared to the weight of the rocket (given in part 2), so you can ignore it in your calculations!

You and your friend would like to experimentally determine a value for g, an object's acceleration due to gravity on Earth. Your friend sets a baseball on the edge of a desk, and you crouch down by the floor, waiting for the ball to drop. She pushes the ball off the desk and yells GO! to signal you to press START your phone's stopwatch app. When the ball hits the floor, you press STOP on the app to stop the timer, and see that the time reads t = 0.606 s. Using a tape measure with markings for cm, you measure the top of the desk to be h = 123 cm from the floor.  Part 1) Assuming the ball started with no initial vertical velocity, calculate the value of g in your experiment symbolically. Assume that g is a positive number.  Part 2) Using your previous symbolic answer and the qualities from the experiment, determine a numeric value for g.  Part 3) What is a reasonable quantitative estimate for your uncertainty in stopping the timer, sigma t? What about your error in measuring the height…