Chapter 12, Problem 157P

1. For a particle in space, the velocity may be defined by the function, (t) = 0.8ti + 12√ej + 5k. Find the velocity and acceleration of the particle at t = 9 seconds and correctly present each as cartesian vectors.

The drag-free motion of a particle is defined by the following component equations in the X, Y Cartesian coordinate system: 1. 2 h = (Vo cos α) t and Ty = (Vo sin α) t -, 1 2 where Vo-200 m/s, α-60° and g-9.81 m/s. At t-40 s, find the components of the velocity and acceleration vectors in the X, Y Cartesian coordinates. Draw vector diagrams of the velocity and acceleration vectors in the Cartesian coordinates, including the unit vectors. 2. The velocity components of a particle are given as The initial conditions of position are r t0)y(t). Att 1s: (a) Find the components of the position and acceleration vectors in the Cartesian coordinates. (b) Determine the velocity and acceleration components in the Polar coordinates (c) Draw vector diagrams to demonstrate that the same velocity and acceleration vectors are obtained for both the Cartesian and Polar coordinate systems. Use the vector diagrams to show the vector components, unit vectors, and units.

The velocity distance graph for the car moving on a linear path is shown in Figure 3. Determine the rate of change of velocity of car at distance (P)=100 m and distance (P)=200 m. Also draw the acceleration distance diagram.

An object is made to travel along a path y = x³ and an observer sees that it is travelling horizontally at i = 24t3 " where t is in seconds. What is the magnitude and vector equation of the acceleration and velocity after half a second?

please do it clearly and fast and all three parts

A cannon is fired so that a cannonball is launched with a horizontal velocity of +27.5 m/s and a vertical velocity of 14.5 m/s up. Find the resultant velocity (v and e) of the cannon ball when it is launched. Give your answer to 3 significant figures. Use 5 significant figures in any intermediate calculations. The resultant velocity is Number m/s and Number ° up from the positive axis.

A particle moves in a circle with a diameter of 120 cm. If its linear velocity is given by v = 4.5t where v is in mps and t is in s, find the radial, tangential and the resultant acceleration of the particle.

A particle travels along the circular path x2 + y2 = r2. If the y component of the particle's velocity is Vy = 2r cos 2t, determine the x and y components of its acceleration at any instant.

A point P starts moving from A along a circular path with radius r. Its motion is described by the relation s = c t2. Determine: a) the velocity components vx(t) and vy(t), b) the velocity at point B, c) the tangential acceleration at(s) and the normal acceleration an(s).