The positon vector r of a particle of mass 2 kg at time / seconds is given by r= [(2 sin 2t) i + (1 - cos 2t) j] m. Find (a) the velocity and the acceleration of the particle when / (b) the kinetic ernegy of the particle when /-, (c) the force acting on the particle when /=, (d) the values of t where 0 sts for which the velocity of the particle is perpendicular to its acceleration.

The positon vector r of a particle of mass 2 kg at time / seconds is given by r= [(2 sin 2t) i + (1 - cos 2t) j] m. Find (a) the velocity and the acceleration of the particle when / (b) the kinetic ernegy of the particle when /-, (c) the force acting on the particle when /=, (d) the values of t where 0 sts for which the velocity of the particle is perpendicular to its acceleration.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 2.10CYU: Check Your Understanding Verify that vector v V obtained in Example 2.14 is indeed a unit vector by...

See similar textbooks

Similar questions

Super Mario is preparing to jump into a pipe. During motion analysis of his awesome pipe jumping abilities, just prior to his jump, he has flexed his knee. Coordinates of his legs were measured. His hip point is at (3,8), his knee is at (9,4), and his ankle is at (7,-1). The coordinates are measured in cm. a) how long is his thigh? b) how long is his shank (lower leg)? c) What is the angle of his knee joint?
the Phpical inev tia tensar car tes ian Cordinate in the system is efual to fi : I1 03 221 L31 2 if the velacity vector of this anguler object is ū sw(isak) what is the kinetic eneryy of this object egual to ? 1) Iut 2)7 Iu? 4) 25 Iw?
A 1500 kg car was moving +31 "½ (E) in the exit lane, but 7.0 s later only +10 m/ (E) at the S exit ramp. b) compute the car's displacement (vector!) if its acceleration was constant during that interval O +217 m (E) +70 m (E) O +143.5 m (E) O +290.5 m (W) O +73.5 m (E) O -73.5 m (W)
6.00k, with t in seconds and r in meters. An electron's position is given by 7 = 4.00tî – 5.00t2 ĵ + (a) In unit-vector notation, what is the electron's velocity v (t)? (Use the following as necessary: t.) V (t) = m/s (b) What is v in unit-vector notation at t = 5.00 s? v(t = 5.00) = m/s (c) What is the magnitude of v at t = 5.00 s? m/s (d) What angle does v make with the positive direction of the x axis at t = 5.00 s? ° (from the +x axis)
A cannon ball is shot into the air such that itsheight h, in metres, after time t, in seconds,can be modelled by the function ht=-9.8 t2+78.4 t+1.5.
Is it possible to add a scalar quantity to a vector quantity?
Check Your Understanding For vector in a rectangular coordinate system, use Equation 2.29 through Equation 2.32 to show that and .
If A + B = 0, the corresponding components of the two vectors Aand Bmust be (a) equal, (b) positive, (c) negative, (d) of opposite sign.
(b) Determine the acceleration at t = 2.0 s. SOLUTION (Use the following as necessary: t and At.) Knowing that the initial velocity at any time t is v, xi (39 – 0.8t2) m/s, find the velocity at any later time t + At: m/s Find the change in velocity over the time interval At: Δν. m/s To find the acceleration at any time t, divide this expression by At and take the limit of the result as At approaches zero: Av a = lim At-0 m/s? Δε Substitute t = 2.0 s (Enter your answer in m/s. Indicate the direction with the sign of your answer.): m/s?
The horizontal distance d, in meters, travelled by a ball that is kicked at an angle, 0, with the ground is modelled by the formula d = 2(v.) cos? 0–1 initial velocity of the ball, in meters per second, and g is the force of gravity (9.8m/s2). Which expression is identical to the given formula? , where v, is the 1,2 cos e =PO ," cos 20 = P O no correct answer U, sin 20 d v, tan 20
In the presence of friction, the descending velocity v of the particle is determined as follows. mxdv/dt = mg-yv ap m =mg -yv dt (a) Predict v through dimensional analysis. (b) Solve the differential equation directly and compare it with the dimensional analysis. please. help...
An object of mass m is projected with initial velocity v0 at an angle of θ degrees to thehorizontal. Assuming that the surrounding air offers resistance kv to motion, where v isthe velocity of the object. Discuss the motion of the object in terms of maximum height,maximum horizontal distance. With appropriate choice of parameters(θ, v0, k and m) plotx + y as a function of time where x and y are horizontal displacement from the origin and theheight of the object at time t respectively