A particle moves along the z-axis according to r(t) = 4t - 7t² m. a. What is the instantaneous velocity at t = 3 s? m/s b. What is the instantaneous speed at t = 3 s? m/s c. What is the average velocity between t=2s and t = 3 s? m/s

Two spheres are launched horizontally from a 1.2 mm -high table. Sphere AA is launched with an initial speed of 4.5 m/sm/s . Sphere BB is launched with an initial speed of 2.5 m/sm/s . A. What is the time for the sphere AA to hit the floor? Express your answer using two significant figures.   B. What is the time for the sphere BB to hit the floor? Express your answer using two significant figures.

We know that the moon Callisto revolves around Jupiter during a period of 17.0 days.17.0 days. The average distance from the center of Jupiter to the center of Callisto is 1.95×109 m.1.95×109 m. What is the acceleration ?a of Callisto due to its motion around Jupiter?

2. a. A particle is undergoing a uniform rectilinear motion and the displacement as a function of time is given by r(t) = 6tª- 2t³ -12t²+3t+3 where r is in meters and t is in seconds. b. What is a uniform rectilinear motion? c. Find the average acceleration of the particle between t = 0 and t = 2s d. When is the acceleration zero? = 3. The position of a particular particle as a function of time is given by r 9.60t i+ 8.58 j - 1.00t² k) m. Determine the particle's velocity and acceleration as a function of time.

. A stone is thrown from level zero at 30° above horizontal. It lands at the same level 20 m away.a. What is the initial speed of the stone?b. What is the maximum height that it reaches during the flight?c. How long does the whole flight take?

A helicopter blade spins at exactly 110 revolutions per minute. Its tip is 9.5 m from the center of rotation. A. What is the average speed of the blade tip in the helicopter's frame of reference, in meters per second?  B. What is the average velocity over one revolution, in meters per second?

9: An archer fires an arrow straight up into the air with a speed v0=35.6m/s. Neglect air resistance.   a. Find the maximum height, hℎ, in meters, reached by the arrow.  b.  In terms of known quantities, write an expression for the time the arrow is in the air until it returns to launch height.

A ball is thrown horizontally from a cliff of height 90 meters with an initial speed of 45 m/s. A. How far from the base of the cliff will it strike the ground? B. What is its vertical component of velocity when it strikes the ground? C. What is its speed when it strikes the ground?

A boat searching for underwater archaeological sites in Palawan sea moves at 4 knots and follows the path r = 10θ, where θ is in radians. A knot is 1 nautical mile or 1852 m/hour. When θ = 2π radians, find the magnitude of the velocity. a. 1.81 m/s b. 2.06 m/s c. 1.18 m/s d. 2.852 m/s

At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 19 m/s. When she lands, where will she find the ball? Ignore air resistance. Ax m