Answer to Question #261299 in Physics for jay

Question

At t = 0, a particle starts from rest at x = 0, y = 0, and moves in the xy plane with an acceleration a =  

(4.0i + 3.0j) m/s2. Determine: 

     a) the x and y components of velocity. [ANS v = (4.0ti + 3.0tj) m/s] [INTEGRATE] 

    b) the speed of the particle. [ANS = 5.0t m/s] 

    c)    the position of the particle as a function of time. [ANS s = (2.0t2i + 1.5t2j) m] [INTEGRATE] 

    d) the speed and position vector of the particle at t = 2.0 s. [ANS speed = 10 m/s, s = (8.0i +6.0j) m]  

 

Answer 1

a) $\vec a=d\vec v/dt\to d\vec v=\vec a\cdot dt\to \vec v=\int{\vec a\cdot dt}=4t\vec i+3t\vec j$

b) $v=\sqrt{(4t)^2+(3t)^2}=5t$

c) $\vec v=d\vec s/dt\to \vec s=\int{\vec v\cdot dt}=2t^2\vec i+1.5t^2\vec j$

d) $v=5t=5\cdot2=10\ (m/s),\ \ \vec s=2\cdot2^2\vec i+1.5\cdot2^2\vec j=8\vec i+6\vec j$