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The acceleration of a particle moving only on a horizontal xy plane is given by
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FUNDAMENTALS OF PHYSICS - EXTENDED
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- An object has position given by the vector r = [3.0m + (6.0m/s)t] i + [2.0m - (2.0m/s2)t2] j, where quantities are in SI units. What is the speed of the object at t = 3.0s?arrow_forwardA particle moving with an initial velocity v, = (10m/s)î and initial position 7, = (4m)î + (2m)j, undergoes an acceleration ở = 2t²î + 4ĵ in SI units. For t = 10 s; a) Calculate the velcoity v= vxI+ vy®. b) Calculate the position r= x+ y. c) What are the magnitudes of the velocity and the position vector of the particle? d) Find also the angle each vector is making with the x-axis at that time.arrow_forwardThe velocity of a particle is given by v = {16t?i + 4t³j + (5t + 2)k} m/s, where t is in seconds. If the particle is at the origin when t=0, determine the magnitude of the particle's acceleration when t=2s. Also, what is the x, y, z coordinate position of the particle at this instant?arrow_forward
- The position vector 4.70t|i+ [et + ft2 locates a particle as a function of time t. Vector is in meters, t is in seconds, and factors e and f are constants. The figure gives the angle e of the particle's direction of travel as a function of time (0 is measured from the positive direction of the x axis). What are (a) factor e and (b) factor f, including units? 20° 0° 10 20 -20° t (s) (a) Number Units (b) Number Unitsarrow_forwardFrom the origin, a particle starts at t = 0 s with a velocity vecv=7.0hatim//s and moves in the xy plane with a constant acceleration of veca=(-9.0hati+3.0hatj)m//s^(2). At the time the particle reaches the maximum x coordinate, what is its (a) velocity and (b) position vector?arrow_forwardAn object moves in the x-y plane with coordinates given as a function of time by: x(t) = Rcos(wt) y(t) = Rsin(wt) where R and w are constants. What is the velocity vector of the object at any time t? v = - Rosin (mt)i + Rwcos (mt)j Ov=Rcos (ot)i - Rsin (mt)j Ov= - Rsin (ot) i+ Rcos (ot)j v = Rwcos (ot)i- Rosin (@t)jarrow_forward
- The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 31ĵ, where a is in meters per second- squared and t is in seconds. At t = 0, the position vector = (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector 7 = (6.40m/s)i + (3.20m/s) j. At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number i (b) Number i î+ Units i ĴUnitsarrow_forwardThe acceleration of a particle moving only on a horizontal xy plane is given by á = 3t i+4t j, where á is in meters per second-squared and t is in seconds. At t = 0, the position vector is 7 = (20 m) i+(40 m) j and the velocity vector v = (5 m/s) i+(2 m/s) j. Find expressions for the (a) x and (b) y component (in meters) of the position of the particle at time t. (c) What is the angle between its velocity and the positive direction of the x axis at time t? (а) х %3D 5t+20) i m Edit (b) y = Edit (c) e = Edit Click if you would like to Show Work for this question: Open Show Workarrow_forwardA particle leaves the origin with an initial velocity ✓ = (7.83î) m/s and a constant acceleration à = ( − 1.38î – 2.16ĵ) m/s² When the particle reaches its maximum x coordinate, what are (a) its velocity, (b) its position vector? (a) Number i (b) Number i Ĵ Units i Ĵ Unitsarrow_forward
- The position vector 7 = (4.30t)î + (et + ft²) locates a particle as a function of time t. Vector is in meters, t is in seconds, and factors e and fare constants. The figure gives the angle of the particle's direction of travel as a function of time (0 is measured from the positive direction of the x axis). What are (a) factor e and (b) factor f, including units? 20° 0° -20° 10 t(s) 20arrow_forwardA particle moving in the x-y plane has a velocity v = 7.80i + 2.97j m/s at a certain instant. If the particle then encounters a constant acceleration a = 0.88j m/s², determine the amount of time which must pass before the direction of the tangent to the trajectory of the particle has been altered by 33º. Answer: t = i Sarrow_forwardA particle has a position function r ⃗ (t) = cos(1.0t)i ^ + sin(1.0t)j ^ + tk ^ , where the arguments of the cosine and sine functions are in radians. (a) What is the velocity vector? (b) What is the acceleration vector?arrow_forward
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