The equation bold r (t )equals(8 t plus 9 )bold i plus (2 t squared minus 8 )bold j plus (6 t )bold k is the position of a particle in space at time t. find the particle's velocity and acceleration vectors. then write the particle's velocity at t equals 0 as a product of its speed and direction.

If a substance is in the gas phase, which of qualities of the gas will stay constant? a: volume b: mass c: shape d: position of particles

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

Neurons are components of the nervous system of the body that transmit signals as electrical impulses travel along their length. these impulses propagate when charge suddenly rushes into and then out of a part of the neutron called an axon. measurements have shown that, during the inflow part of this cycle approximately 5.6x10^11 na per meter, each with a charge of e enter the axon. how many coulombs of charge enter a 1.10 cm length of axon during this process