Ablock of mass m is undergoing shm on a horizontal, frictionless surface while attached to a light, horizontal spring. the spring has force constant k, and the amplitude of the shm is a. the block has v = 0, and x = +a at t = 0. it first reaches x = 0 when t=t/4, where t is the period of the motion. a) in terms of t, what is the time t when the block first reaches x=a/2?
b) the block has its maximum speed when t=t/4. what is the value of t when the speed of the block first reaches the value vmax/2?

A250-n box is at rest on a frictionless horizotal floor. then a person shoves the box with a non-zero force of magnitude p. which statement best describes the relationship betweeen p and the motion of the box after it was shoved? -the box will not move when p< 250n but otherwise will accelerate at a constant rate that is directly proportional to p - the box will begin moving at a speed that is directly proportional to p, then will gradually slow to a halt -the box will move with constant velocity at a speed that is directly proportional to p -box will accelerate across the floor at a constant rate that is directly proportional to p

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)

Calculate 9 ∙ 10-5 divided by 3 ∙ 10-9. (box after the "10" in answer is for the