A particle's position is given by × = 14.0 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) What is its velocity at t = 1s? (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 "O". (f) Is there a time after

In a room, a boy throws a ball up. (a) Will the ball hit the bulb in the ceiling, 4 meters above the floor, if it leaves the boy's hand at 9.0 m/s? Justify your answer. (b) If your answer in (a) is yes, how much time does it take the ball to reach the ceiling? If your answer in (a) is no, how much time does it take the boy to catch the ball? Ignore air friction.

An object is launched at 9.8 meters per second (m/s) from a 171.5-meter tall platform. The function that represents the object's height s at time t seconds after launch is s(t) = −4.9t2 + 9.8t + 171.5, where s is in meters. When does the object strike the ground?

A rodeo horse is running around a corral at a speed of 300 ft/s. Let x(t) be the distance of the horse from the third barrel and y(t) his distance from the fourth. (see figure; note that the distance between barrels is 900 řt). At what rate is the horse's distance from the fourth barrel changing at the instant when he is 200 ft from the third? 2 1 3 4

Suppose a migrating bird flies at a constant altitude of 5 km, with a velocity of 42 km/h. At time t = 0 the bird passes directly above a radar station, where t is measured in hours. (a) How fast is the distance between the bird and the radar station changing after 10 minutes? Round your final answer to 2 decimal places and provide units. (b) How fast is the distance between the bird and the radar station changing at time t = 0, i.e. when the bird is directly above the radar station? Is this reasonable? Explain briefly.

Make a motion chart for a cannonball launched with an initial speed of 20m/s. Neglect drag and the initial height of the cannonball. After the ball lands on the ground enter zero for all speeds and heights if necessary. Use regular metric units (ie. meters). Round all speeds to nearest whole number, if necessary. |a| = 10 m/s? t |v| m/s m 20 10 15 10 20 15.9 4 20 1.6 5 direction of motion at 3s: down

IXFQP A police car traveling 95.0 km/h is traveling west, chasing a motorist traveling at 80.0 km/h. What is the velocity of the motorist relative to the police car? What is the velocity of the police car relative to the motorist? If they are originally 250 m apart, in what time interval will the police car overtake the motorist? (Only the third part appears on the answer sheet.) [S] E08 04.35] 5. A. 53.76 s D. 64.87 s 48.63 s E. 65.66 s 60.00 s F. 74.72 s IXXKI MacBook Pro & 7 2 W ARCH B. C. 1--1 #3 E 54 $ R % 5 T Y U *00 8 ( 9 -O O 0 1 P + {

A particle moving along a straight line has initial velocity v(0) = 1 m/s, and acceleration a(t) = sin(I-t) + cos(t+1) (in m/s?). (a. Find the velocity at time t. (b) Find the average velocity during the time interval [I, 211]. (c) Find the distance traveled during the time interval [1, 2I].

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".

Piolo's car is traveling initially at 20k(m)/(h). What is its final velocity if he accelerates the car to 3.3k(m)/(h^(2)) for 3h ?