Question

What are two assumptions to analyze the motion, if the ball moves in a curved path? A particle starts from the origin at t=0 with an initial velocity having an x component of 20 m/s and a y component of – 15 m/s.The particle moves in the xy plane with an x component f acceleration only, gives by a_x= 4.0 m/s^2.Calculate the velocity and speed of particle at t = 5 s. *

Answer 1

By definition, the velocity of the particle under a constant acceleration is:

$$\mathbf{v} = \mathbf{v}_0 + \mathbf{a}t$$

where $\mathbf{v}_0 = (20, -15)\space m/s$ is the vector of the initial velocity, $\mathbf{a} = (4,0)\space m/s^2$ is the vector of the acceleration, and $t =5s$ is the time. Thus, obtain:

$$\mathbf{v} = (20, -15)\space m/s \space +\space (4,0)\space m/s^2\cdot 5s = (40,-15)\space m/s$$

The speed is the magnitude of the velocity:

$$v = \sqrt{(40)^2 + (-15)^2} \approx 42.7m/s$$

Answer. The velocity is $(40,-15)\space m/s$., the speed is 42.7 m/s.