Mechanics | Relativity Answers

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1.a particle moves on a circle in accordance w/ the eqn. s=t^4 - 8t, where s is the displacement in feet measured along the circular path and t is in seconds. 2 seconds after starting from rest the total acceleration of the particle is 48√2 ft/sec^2. Conpute for the radius of the circle.
2. As you drive down the road at 17 m/s, you press at the gas pedal and speed up with the uniform acceleration of 21.12 m/s^2 for .65 s. If the tires on your car have a radius of 33 cm what is their angular displacement during the period of acceleration

The moment of inertia of a annular disc of mass M,the inner diameter R1 and outer diameter is R2 about perpendicular to the axis is

A certain sprinter has a top speed of 10.6 m/s. If the sprinter starts from rest and accelerates at a constant rate, he is able to reach his top speed in a distance of 10.1 m. He is then able to maintain his top speed for the remainder of a 100 m race. (a) What is his time for the 100 m race? (b) In order to improve his time, the sprinter tries to decrease the distance required for him to reach his top speed. What must this distance be if he is to achieve a time of 10.3 s for the race?

An automobile driver increasing the speed at a constant rate from 45 km/h to 58 km/h in 0.49 min. A bicycle rider speeds up at a constant rate from rest to 13 km/h in 0.49 min. What are the magnitudes of (a) the driver's acceleration and (b) the rider's acceleration?

A proton moves along the x axis according to the equation x = 62 t + 14 t^2, where x is in meters and t is in seconds. Calculate (a) the average velocity of the proton during the first 3.0 s of its motion, (b) the instantaneous velocity of the proton at t = 3.0 s, and (c) the instantaneous acceleration of the proton at t = 3.0 s.

The sport with the fastest moving ball is jai alai, where measured speeds can be 296 km/h. If a professional jai alai player faces a ball at that speed and involuntarily blinks, he blacks out the scene for 100 ms. How far does the ball move during the blackout?

A lead ball is dropped in a lake from a diving board 7.32 m above the water. It hits the water with a certain velocity and then sinks to the bottom with the same constant velocity. It reaches the bottom 4.88 s after it is dropped. (a) How deep is the lake? (b) What is the magnitude of the average velocity of the ball for the entire fall? (c) Suppose the water is drained from the lake. The ball is now thrown from the diving board so that it again reaches the bottom in 4.88 s. What is the magnitude of the initial velocity of the ball?

Two subway stops are separated by 1500 m. If a subway train accelerates at 1.2 m/s^2 from rest through the first half of the distance and decelerates at -1.2 m/s^2 through the second half, what are (a) its travel time and (b) its maximum speed?

A car moving with constant acceleration covered the distance between two points 56.2 m apart in 5.32 s. Its speed as it passes the second point was 14.8 m/s. (a) What was the speed at the first point? (b) What was the acceleration? (c) At what prior distance from the first point was the car at rest?

A rocket-driven sled running on a straight, level track is used to investigate the effects of large accelerations on humans. One such sled can attain a speed of 1640 km/h in 2.00 s, starting from rest. Find (a) the acceleration (assumed constant) in terms of g and (b) the distance traveled.