The position of a car as a function of time t, with t>0 and expressed in seconds, is r(t)=((5.98t2+0.139t3−0.0149t4)i^+(0.523t2+0.0122t3−0.00131t4)j^)ft. Determine the velocity, and speed, and acceleration of the car for t=17.5 s. (Round the final answers to four decimal places. Include a minus sign if necessary) The expression of the velocity of the car is v(17.5 s)=(j^)ft/s. The speed of the car is ft/s. The expression of the acceleration of the car is a(17.5 s)=(i^+j^t/s2.
Suppose that a highway exit ramp is designed to be a circular segment of radius ρ=130 ft. A car begins to exit the highway at A while traveling at a speed of 65mph and goes by point B with a speed of 25mph. Compute the acceleration vector of the car as a function of the arc length s, assuming that between A and B the speed was controlled so as to maintain constant the rate dvids. (Round the final answers to four decimal places. Include a minus sign if necessary.) The acceleration vector of the car is a=((ft2)+(s−2)s)ut+((ft2)−(s−2)+( 1s−2)s2)un
A race boat is traveling at a constant speed vo =154mph when it performs a turn with constant radius ρ to change its course by 90 as shown. The turn is performed while losing speed uniformly in time so that the boat's speed at the end of the turn is vf=125 mph. If the maximum allowed normal acceleration is equal to 2g, where g is the acceleration due to gravity, determine the tightest radius of curvature possible and the time needed to complete the turn. (Round the final answers to four decimal places.) The tightest radius of curvature possible is f. The time needed to complete the turn is S.
r=r0(1+rt) and θ=θ0τ2t2 where r0=3ft,θ0=1.2 rad, t=20 s, and t is time in seconds. Determine the velocity and the acceleration of the particle for t=39.5 s and express the result using the Cartesian component system formed by the unit vectors i^ and j^. (Round the final answers to four decimal places. Include a minus sign if necessary.) The velocity of the particle is v=(i^+ft/s. The acceleration of the particle is a=(i^+j^)ft/s2.
Particle A slides over the semicylinder while pushed by the arm pinned at C. The motion of the arm is controlled such that it starts from rest at θ=0,ω increases uniformly as a function of θ, and ω=0.5 rad/s for θ=452. Letting R=4 in. determine the speed and the magnitude of the acceleration of A when Φ=34∘. (Round the final answers to four decimal places.) The speed of A is ft/s. The magnitude of the acceleration of A is ft2
The pulley system shown is used to store a bicycle in a garage. If the bicycle is hoisted by a winch that winds the rope at a rate vo = 6.5 in.15, determine the vertical speed of the bicycle. (Round the final answer to four decimal places.) The vertical speed of the bicycle is ftis.
In the pulley system shown, the segment AD and the motion of A are not impeded by the load G. Assume all ropes are vertically aligned. Determine the velocity and acceleration of the load G if v0=3.75ft/s and a0=1ft/s2. (Round the final answers to four decimal places. Include a minus sign if necessary.) π0] The velocity of the load G is jt^/s. The acceleration of the load Gis jft/s2.
The position of a car as a function of time t, with t>0 and expressed in seconds, is r(t)=((5.98t2+0.139t3−0.0149t4)i^+(
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The position of a car as a function of time t, with t>0 and expressed in seconds, is r(t)=((5.98t2+0.139t3−0.0149t4)i^+(
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