At t=0, a particle starts from rest at = 0, y = 0, and moves in the xy plane with an acceleration a = (4.0₁ + 3.0ĵ)m/s². Assume t is in seconds. Part A Determine the component of velocity as a function of time t. Express your answer using two significant figures. ΜΕ ΑΣΦ vx(t) = Submit Request Answer Part B ? m/s Determine the y component of velocity as a function of time t. Express your answer using two significant figures. ΜΕ ΑΣΦ vy(t) = ? m/s
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- Problem 5. The velocity of a particle moving along the x -axis is defined by v = kx°- 4x² + 6x , where v is in m/sec, x in meters , and k is constant. If K = 1, compute the value of acceleration after x= 2meters. Find: 10. a = ?2.68 0. CALC An object's velocity is measured to be v,(1) = a – Bt², . 4.00 m/s and B = 2.00 m/s. At t = 0 the object is at x = 0. (a) Calculate the object's position and acceleration as functions of time. (b) What is the object's maximum positive displacement from the origin? where a =find the area velocity of a particle moving along the path r= a cos w t i + b sin w t j, where a, b and w are constant and t is time. template: (1/2)a b w k.
- If you want to go by train from Los Angeles to New York, you must make a stop. First, you musttravel 1800 miles East to reach New Orleans. Then you must travel 1300 miles at 45◦ North of Eastto reach New York.(a) Graph the vectors for each segment of the trip and the resulting displacement. Each tick markshould represent 300 miles.(b) If you flew directly from Los Angeles to New York, how far would the flight be? Please show your workGiven vector A = (3.00i - 2.00j)m and vector B = (-2.00i + 2.00j)m determine vector C if C = 3A - B. Answers should have three significant figures and each component should have units. Remember to leave a space between your numerical values and the units.A quadratic fit is done on a distance versus time graph of an object with constant acceleration using a computer program. The distance is in meters and the time in seconds. The form of the quadratic fit is y (z)= Az + Bz + Cand the fit parameters were found to by A-0.5, B-2 and C-3. What is the acceleration? 1.5 m/s 0.25 m/s 0.5 m/s -2 m/s 1 m/s 3 m/s OO0O C
- = A polo ball is hit with a mallet off the edge of a cliff. Its x- and y-coordinates as functions of time are given by x = 16.8t and y meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the ball's position as a function of time (in m), using the unit vectors î and ĵ. (Give the answer in terms of t.) r= By taking derivatives, do the following. (b) Obtain the expression for the velocity vector v as a function of time (in m/s). (Give the answers in terms of t.) m (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). m/s² II m/s to || (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the polo ball at t = 2.85 s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s².) 3 3.72t - 4.90t2, where x and y are in m/s m/s²An adventure racer ran 1.7 km north, then 3.2 km 63° to the south of due east, then 1.4 km west. She completed the trip in 2 hr: 5 min :8 s. What was the magnitude of her average velocity over the entire trip in m/s? Express your answer in metres/second to two decimal places (do not include units in your answer).v sin 20 gives the distance x travelled (in feet) by a projectile launched from 32 The formula r% = the ground, with initial velocity v (in feet/sec) and initial angle 0 (in radians or degrees). a. Write an expression for the total differential in x. b. Use the total differential to estimate the error in calculating the range of a projectile with initial velocityv 100 ft/sec and initial angle 0= 50 degrees, with measurement errors of dv = t10 ft/sec (for velocity) and d6==5 degrees (for the initial angle). (Note: remember to use radians for the differential in 0.)
- Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 21 feet high? Round to three significant digists. Recall that the volume of a right circular cone with height h and radius of the base r is given by V = r²h ft minthe coordinates of an object moving in an xy plane vary with the time according to the eqations x=-7.85 sin w(omega)t, and y=4-7.85 cosw(omega)t. W(omega) is constant , x,y - in meters. And t in seconds. Write expressions for the possition,velocity and acceleration vectors of the object at any time t>0.An archaeologist is surveying a cave. She follows a passage 150 m west, then 110 m southeast, and then 185 m 30 deg east of north. After a fourth unmeasured displacement, she finds herself back where she started. What is the magnitude and direction of this unmeasured displacement?