When a particle is projected vertically upwards with an initial velocity of ϑ0, it experiences an acceleration shown below, where g is the acceleration due to gravity, k is a constant and ϑ is the velocity of the particle. Determine the maximum height reached by the particle in m when k = 0.5 and initial velocity ϑ0 =10 m/s.

At t = 0 a particle at the origin has a velocity of 15.1 m/s at 36° above the horizontal x axis. At t = 5.00 s it is at x = 21.0 m and y = 35.0 m and its velocity is 30.0 m/s at 53° above the horizontal. Find: (a) its average velocity; (b) its average acceleration

A particle has an acceleration of a=2i + (t-1)j The velocity at t=0 is v0=-2i + 0j and is at the origin at t=0   What is the y  position when the x velocity is zero? answer in m

I need help here please

The x-coordinate of a particle in curvilinear motion is given by x= 2.1t³ -2.4t where x is in feet and t is in seconds. The y-component of acceleration in feet per second squared is given by ay = 2.0t. If the particle has y-components y = 0 and vy= 2.2 ft/sec when t = 0, find the magnitudes of the velocity v and acceleration a when t = 2.7 sec. Sketch the path for the first 2.7 seconds of motion, and show the velocity and acceleration vectors for t = 2.7 sec. Answers: V = i a= i ft/sec ft/sec²

The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line.Constants b and c are positive. a(t) = bt + c,    and initial velocity v(0)> 0 ; where    0 ≤ t ≤ x (a) Find the velocity at time t.v(t) =         m/s(b) Find the distance traveled during the given time interval.distance (t) =         m

A ball is throw hoard from the ground with  initial velocity vi= 14 m/s and reaches height of h above the ground before falling back down. Take the upwards direction to be positive. Neglect air resistance. (F) Calculate the value of delta t in seconds. (G) What is the total displacement, in meters, of the ball going through its entire motion: traveling from the ground to the top then falling back to the ground? (H) Enter an expression for the total time of flight of the ball: the time from when it is launches to when it lands ba on the ground. (I) Express this time in terms of vi and a. Calculate the value of delta t tot in seconds. (J) Enter an expression for delta t tot in terms of the variable delta t tot in terms of the variable delta t, the time of ascent from the ground to the top of the trajectory. (K)  Express the velocity of the ball right before it hits the ground, vf, in terms of vi, delta t and a. (L) Express vf in terms of vi.