An object moves with an initial velocity v 3.40j m/s and an acceleration à - 2.9
ID: 1784943 • Letter: A
Question
An object moves with an initial velocity v 3.40j m/s and an acceleration à - 2.90î m/s2. Assume the object is initially at the origin (a) What is the position vector of the object as a function of time? (Express your answer in vector form. Use the following as necessary: t.) r(t) = (b) What is the velocity vector of the object as a function of time? (Express your answer in vector form. Use the following as necessary: t.) v(e)- m/s (c) What is the position of the object at time t = 2.50 s? (Express your answer in vector form.) r(2.50 s) = (d) What is the speed of the object at time t 2.50 s?Explanation / Answer
Given
velocity vector is V = 0 m/s i + 3.4 m/s j
acceleration vector is a = 2.9 m/s2 i + 0 m/s2 j
we know that the integration of velocity vector with respect to time is the position vector as a function of time
a)
that is r(t) = integral of v(t)dt
= integral ((0 m/s i + 3.4 m/s j )*dt)
= 3.4 t m/s j
c) the position of the object at time t= 2.5 s is, r(3.5) = 3.4*2.5 m = 8.5 m
b) Velocity vector as a function of time is v(t) = integral of a(t) dt
v(t) = integral of (2.9 m/s2 i + 0 m/s2 j) dt
v(t) = 2.9*t m/s i
d) speed of the object at time t= 2.5 s
v(2.5) = 2.9*2.5 m/s = 7.25 m/s