Find the velocity, acceleration, and speed of a particle with the given position function.r(t)=(2cos t,3t,2sin t) 相关知识点: 试题来源: 解析 r(t)=(2cos t,3t,2sin t)\ ⇒ \ v(t)=r'(t)=(-2sin t,3,2cos t), a(t)=v'(t)=(-2cos t,0,-2sin t), v(t) =√ (...
Suppose that a(t), the acceleration of a particle at time t, is given by a(t)=4t-3 that ν (1)=6 and tha f(2)=5 , where f(t) is the position function. Find v(t) and f(t). ___ 相关知识点: 试题来源: 解析 f(t)= 23t^3- 32t^2+7t- (25)3 反馈 收藏 ...
Find the position function if the acceleration function is a(t) = 10 \sin(t) + 1 , the initial velocity is v(0) = -7 and the initial position is s(0) = 6 . Given the acceleration, a (t), the initial velocity, ...
The position of a body at any time T is given by the displacement function S=t3-2t2-4t-8.Find its acceleration at each instant time when the velocity is zero. 相关知识点: 试题来源: 解析 a=8δ=t^3-2t^2-4t-8 v=ds/dt=3t^2-4t-4 a=dv/at=6t—4 V=0 3xt^2-4xt-4=0 3...
Given the velocity {eq}\mathbf v(t) = \langle e^t, 6t, \cos t \rangle {/eq} and the initial position {eq}\mathbf r(0) = \langle 4,1,6 \rangle {/eq}, find the position function {eq}\mathbf r(t) {/eq} Position,...
Find the position of the particle. s(t) a(t) = 2t + 3, s(0) = 8, v(0) = -4 Position Function: We will find the position function from the acceleration function by integrating the function twice as acceleration is the rate of change of velo...
Here is another simple way to find the position ThemeCopy t = 0:0.01:10; % consider a time vector for ball displacement (say 10s) x0 = 10; v0 = 15; a = -9.81; % acceleration x = x0+v0*t+0.5*a*t.^2; hold on plot(t,x); yli...
The velocity function {eq}v(t) {/eq} of a moving particle is the rate of change of displacement function {eq}s(t) {/eq} with respect to time. The acceleration function {eq}a(t) {/eq} is the rate of change of velocity function {eq}...
An object moves in a straight line with position given by s(t)=t^2-4t+3 cm from an origin , wher t is in seconds, t≥0 . (1)Find expressions for the object's velocity and acceleration at any instant and draw sign diagrams for each function. (2)Find the initial conditions and e...
(a) Determine the acceleration and position of the bullet as a function of time when the bullet is in the barrel.(b) Determine the length of time the bullet is accelerated.(c) Find the speed at which the bullet leaves the barrel.(d) What is the length of the barrel? 扫码下载作业帮...