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- The coordinates of an object moving in the xy plane vary with time according to the equations x=25.00sinωt and y=4.00−5.00cosωt, where v is a constant, x and y are in meters, and t is in seconds. (a) Determine the components of velocity of the object at t=0. (b) Determine the components of acceleration of the object at t=0. (c) Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t>0. (d) Describe the path of the object in an xy plot.arrow_forwardDr. B takes her dog ada on a walk. they start out heading south for 0.75 miles. then they turn left 30 degrees and they continue to walk for another 11 mile. Finally they turn right 9o degrees and they walk 1.9 miles. The whole walk takes 45 minutes. What is the average speed of Dr.B and Ada on their walk? give your answer in m/s. What is the direction of the total displacement vector?arrow_forwardA car travels 90 meters due north in 15 seconds. Then the car turns 32° west of north and travels 40 meters. What is the magnitude and direction of the car's resultant displacement? To answer this problem, what two methods will give us the accurate answer?arrow_forward
- A jeep travels a distance d=22.1m in the positive x direction in a time t1=20.2s, at which point the jeep brakes, coming to rest in t2=7.38s. 1. What was the jeep's instantaneous velocity in the horizontal direction, in meters per second, when it began braking? 2. Using the result from question 1, what was the jeep's horizontal component of acceleration, in meters per squared second, during the braking period?arrow_forwardYou are exploring a planet and drop a small rock from the edge of a cliff. In coordinates where the +y direction is downward and neglecting air resistance, the vertical displacement of an object released from rest is given by y − y0 = 1/2gplanett2, where gplanet is the acceleration due to gravity on the planet. You measure t in seconds for several values of y − y0 in meters and plot your data with t2 on the vertical axis and y − y0 on the horizontal axis. Your data is fit closely by a straight line that has slope 0.300 s2/m. Based on your data, what is the value of gplanet?arrow_forwardAn object's position in the x-direction as a function of time is given by the expression; x(t) = 5t2 + 2t where are quantities have proper SI Units. What is the object's average velocity in the x-direction between the times t = 1.11 s and t = 2.18 s. Just enter the number rounded to 3 significant figures and assume it has proper SI Units.arrow_forward
- Suppose you went for a drive along a long, straight road that runs east-west. Let's define east to be the positive x direction. From your home, you drive east at 30 mi/hr to your friends house for 20 minutes, then at 48 mi/hr east for 10 minutes to the grocery store. Finally, you drive west at 60 mi/hr without stopping to get home. What is your displacement for the entire trip?arrow_forwardA student solving a physics problem for the velocity of an object has applied appropriate physics principles and obtained the expression v=d/t−v0, where d=35.0meter, t=9.00second, and v0 =3.00meter/second. What is the velocity v?arrow_forwardAn object's position in the as a function of time obeys the equation; x(t) = 14.2/t2.17 + 5.1t3 where all constants have proper SI Units. What is the speed of the object in the x direction at t = 1.93 seconds?arrow_forward
- An objects position in the x-direction as a function of time is given by the expression: x(t)=5t^2 + 2t where are quantities have proper SI units. What's the objects average velocity in the x-direction between the times t=1.15s and t=2.07s. (Just enter the number rounded to 3 significant figures and assume it has proper SI units)arrow_forwardSuppose you went for a drive along a long, straight road that runs east-west. Let's define east to be the positive x direction. From your home, you drive east at 30. mi/hr to your friends house for 20. minutes, then at 48 mi/hr east for 10. minutes to the grocery store. Finally, you drive west at 60. mi/hr without stopping to get home. How many minutes will it take to drive from the grocery store to your home (at 60. mi/hr)? Note: Your answer should have the correct number of significant figuresarrow_forwardA boy walks uniformly along the sides of a rectangular park with dimensions 400m x 300m, starting from one corner to the other corner diagonally opposite. Which of the following statements is false?A. His displacement is 700 m.B. His displacement 500 m.C. He has travelled a distance of 700 m.D. His velocity is not uniform throughout the walk.arrow_forward
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