An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration have the same sign on the way up as on the way down?
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- 32. An object moves with constant acceleration 4.00 m/s² and over a time interval reaches a final velocity of 12.0 m/s. (a) If its original velocity is 6.00 m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its original velocity is -6.00 m/s, what is its dis- placement during this interval? (d) What is the total distance it travels during the interval in part (c)?A person falls from a height of 2.0m on earth (a=g=9.8m/s2). What acceleration is necessary for them to stop over 30 cm (assuming they bend their knees)? What if they don't bend their knees hence stop over a distance of 1 mm?A cargo helicopter, descending steadily at a speed of 3.8 m/s, releases a small package. Let upward be the positive direction for this problem. (a) If the package is 94 m above the ground when it is dropped, how long does it take for the package to reach the ground? (a) What is the initial velocity of the package? How does it compare to that of the helicopter? What is its sign? What about the magnitude and sign of the acceleration? s(b) What is its velocity just before it lands? (Indicate the direction with the sign of your answer.)
- A block slides across a frictionless horizontal surface with constant acceleration 4.10 m/s2 and over a time interval reaches a final velocity of 10.6 m/s. (a) If its initial velocity is 5.30 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) (b) What is the distance it travels (in m) during this interval? (c) If its initial velocity is −5.30 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) (d) What is the total distance it travels (in m) during the interval in part (c)?A box slides across a frictionless horizontal surface with constant acceleration 4.95 m/s² and over a time interval reaches a final velocity of 11.2 m/s. (a) If its initial velocity is 5.60 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) m (b) What is the distance travels (in m) during this interval? m (c) If its initial velocity is -5.60 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) m (d) What is the total distance it travels (in m) during the interval in part (c)?At a given instant in time, a ball is thrown straight up into the air with a velocity of 5.0 m/s starting from aposition 2.2 m above the ground.(a) What is the position of the ball after 1.0 s?(b) What is the ball’s velocity at this time?(c) What is the maximum height reached by the ball?(d) How far has the ball traveled after 1.0 s?
- A particle's position is given by x = 1.00 - 15.00t + 3t2, in which x is in meters and t is in seconds. (a) What is its velocity at t = 1 s? (b) Is it moving in the positive or negative direction of x just then? (c) What is its speed just then? (d) Is the speed increasing or decreasing just then? (Try answering the next two questions without further calculation.) (e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer "0". (f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give the time t; if not, answer "0".A sports car moving at constant velocity travels 120 m in 5.0 s. If it then brakes and comes to a stop in 3.7 s, what is the magnitude of its acceleration (assumed constant) in m/s², and in g' s(g = 9.8m / (s ^ 2)) ?