3 Find the velocity and position vectors for the particle whose acceleration is given by a' (t) = (6t, et, 4 sinzt) and whose initial velocity and initial position given by ✓(0) = 2 + 2k² and 7²(0) = 2² + 3² + K². are

Q: Find the velocity and acceleration vectors of the particle whose position at time t seconds is given…

A: We have a given position vector of any particle. And we have to find velocity and acceleration…

Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: An object is moving in the air (defying gravity) so that its height after t seconds is given by…

A: Answer :- A)Answer

Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

A:

Q: r(t) = ti+t²j+ + 1 {/f²k 2

A: Solving the problem

Q: ent of acceleration and the principal ovided.

A:

Q: 2. If a particle's position is given by r(t) = <t ₁2 cost, sint), find the IN velocity,…

A: Given: particle position, r→t=t, 2 cos t, sin t We have to find the velocity, acceleration and speed…

Q: WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗…

A: Given :- The curve C parametrized by the vector equation r t = 3 sin t i^ +2 - sin t +cos t  j^…

Q: A floodlight is positioned on the ground shining on a white wall 10 m away. A woman 1.6 m tall…

A:

Q: Find the derivative of the vector function r' (t) = (1/-2t r(t) = n(17t²)i + √13+tj + let k 4e^4

A: Find the derivative of the vector functionr(t)=ln17-t2i+13+tj+1e4tkr'(t)=ddtln17-t2i+13+tj+1e4tk

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

A:

Q: 7. Find the equation for the 'unit tangent vector to the vector-valued function r=. く- I6 Sin(2t),…

A:

Q: A projectile with mass m is launched into the air on a parabolic trajectory. For t >0, its…

A: In the absence of drag or viscous force , the total Mechanical energy of projectile remain constant