The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits

A car is 3.0 km west of a traffic light at t = 0 and 7.0 km east of the light at t = 8.0 min. Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) what are the car’s position vectors at these two times? (b) what is the car’s displacement between 0 min and 6.0 min?

A ball is shot from the ground into the air. At a height of 9.4 m, its velocity is = 7.71+ 6.27 m/s, with i horizontal and upward. (a) To what maximum height does the ball rise? (b) What total horizontal distance does the ball travel? What are the (c) magnitude and (d) angle (below the horizontal; give as negative) of the ball's velocity just before it hits the ground?

Given the displacement vector ? =[3.1?2, 2.0?, 0]:(a) what is the position of the object at time? = 2.1 ? assuming the object started at theorigin?(b) what is the distance the object has traveled at? = 2.1 ??(c) what is the velocity of the object as a functionof time?(d) what is the velocity of the object at ? = 0, ? =2.1 ? and ? = 4.2 ??(e) what is the speed of the object at the timesgiven in part (d). Are the speed evenly spaced?Would you expect this? Why or why not?(f) what is the acceleration of the object at? = 0, ? = 2.1 ? and ? = 4.2 ??