11. An object moving only in the vertical has a constant acceleration of -10 m/s² is initially at rest at a height of 20 m. Through what distance does it fall in the next 2.0 s?
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- 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 0.37 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.1 mm. If the floor is carpeted, this stopping distance is increased to about 1.4 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume 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.3. A ball is thrown vertically upward with a speed of 15.0 m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started?29. The position of a particle for t> 0 is given by r(t) = (3.01² i-7.0t³ -5.0t² k) m. (a) What is the velocity as a function of time? (b) What is the acceleration as a function of time? (c) What is the particle's velocity at t = 2.0 s? (d) What is its speed at t = 1.0 s and t = 3.0 s? (e) What is the average velocity between t= 1.0 s and t = 2.0 s? Solution
- An rock is thrown straight up with an initial velocity of 18.5 m/s. What maximum height will the rock reach before starting to fall downward? (Take acceleration due to gravity as 9.80 m/s2.)A car starts from rest, then accelerates at a constant rate over a distance of 89 m. It then immediately decelerates at a constant rate over a distance of 152 m. The entire trip lasts a total duration of 27.2 s. What were the magnitudes of the car s accelerations for the speedup and slowdown stages respectively? 1. 1.76 m/s^2, then 1.03 m/s^2 2. 3.27 m/s^2, then 5.59 m/s^2 3. 0.65 m/s^2, then 0.65 m/s^2 4. 5.59 m/s^2, then 3.27 m/s^2If the limb is in the road at a distance of 550 meters from where the car begins it’s initial acceleration, will the car hit the limb? Yes or No
- To take off from the ground, an airplane must reach a sufficiently high speed. The velocity required for the takeoff, the takeoff velocity, depends on several factors, including the weight of the aircraft and the wind velocity. A plane accelerates from rest at a constant rate of 5.00 m/s2m/s2 along a runway that is 1800 mm long. Assume that the plane reaches the required takeoff velocity at the end of the runway. What is the time tTOtTO needed to take off? What is the distance d_last traveled by the plane in the last second before taking off?3. In Physics, the height of a free-falling object at a given time t is given by h = –16t² + v,t + h., where v, is the initial velocity, and h, is the initial height. A student throws a ball upward from a height of 48ft, initially at 32 ft/s. What is the maximum height of the ball?1. A particle moves according to the equation x = 2t³ - 2t + 1, where x is in meters and t in seconds. (a) Find instantaneous acceleration as a function of time. (b) Find the value of the instantaneous acceleration at t = 3.5 s.
- A load of bricks is lowered by a crane at a steady velocity of 5.0 m/s when one brick falls off 20.0 m above the ground. 9. What is its speed just before it hits the ground? 10. How long does it take to reach the ground? (Assume acceleration due to gravity is 9.81 m/s²)6. A ball is thrown upward with a velocity of 4.5 m/s. Its speed and the magnitude of its acceleration at the highest point (a) are both equal to zero (b) are given by 9.81 m/s and 0 m/s², respectively (c) are given by 0 m/s and 9.81 m/s², respectively (d) cannot be predicted unless the height is known Answer: 7. Which of the following statements about a projectile is not true? Assume that the air resistance is negligible. (a) Its motion is in two dimensions. (b) The only acceleration is in the vertical direction. (c) Its velocity in the horizontal direction remains the same throughout the flight. (d) The velocity at the highest point of its trajectory is zero. Answer:A car starts from rest, then accelerates at a constant rate over a distance of 80 m. It then immediately decelerates at a constant rate over a distance of 136 m. The entire trip lasts a total duration of 26.0 s. What were the magnitudes of the cars accelerations for the speedup and slowdown stages respectively?