Examples 7 A particle moves in a straight line with a constant acceleration of -4 ft/s2 for 6 s, zero acceleration for the next 4 s, and a constant acceleration of +4 ft/s2 for the next 4 s. Knowing that the particle starts from the origin and that its velocity is -8 ft/s during the zero-acceleration time interval, (a) construct the v-t and x-t curves for 0 sts 14 s, (b) determine the position and the velocity of the particle and the total distance traveled when t = 14 s. a (ft/s²) 4 6 0 -4 10 14 t(s) 12 22

At t = 0 a truck starts from rest at x = 0 and speeds up in thepositive x-direction on a straight road with acceleration aT. At the sametime, t = 0, a car is at x = 0 and traveling in the positive x-direction withspeed vC. The car has a constant negative x-acceleration: acarx = -aC,where aC is a positive quantity. (a) At what time does the truck pass thecar? (b) At what x-coordinate does the truck pass the car?

queston: A particle moves in the x-y plane with an x-component of velocity in meter per second given by vx = 4√t, with t in seconds. The acceleration of the particle in the y-direction in meter per second squared is given by by ay = 4 e(t), with t in seconds. When t-4, y=10, x=4, and vy = 10, (a) Find the equation of the path of the particle and (b) calculate the magnitude of the velocity v of the particle for the instant when its y-coordinate reaches 20 m, and the angle which the velocity makes with the x-axis.

A particle moves along a straight Line with a velocity in (mm/s) given by V=400-16t² where it is in seconds. Calculate the net displacement AX and the total distance traveled during the first 6 seconds of motion.