A particle's position along the x-axis is given by the equation; x(t) = 1t¹ + 1t² +8 where x is in meters and t is in seconds. What is this particles average acceleration between t = 1s and t = 3s? Please express your answer with zero decimal places in units of m/s². Answer:
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- For a short time, the speed v of a car, in m / s, is given by v = at2 + bt3, where t is the time in seconds. The units of a and b are, respectively, a) m/s^2; m/s^3 b) m/s^4; m/s^5 c) s^3/m; s^4/m d) m.s^2; m.s^4 e) m/s^3; m/s^4If an average-size man jumps from an airplane with an open parachute, his downward velocity t seconds into the fall is v(t) = 20(10.2) feet per second. (a) Use functional notation to express the velocity 3 seconds into the fall. Calculate it. ft per sec (b) Explain how the velocity increases with time. Include in your explanation the average rate of change from the beginning of the fall to the end of the first second and the average rate of " change from the fourth second to the fifth second of the fall. This answer has not been graded yet. (c)-Find the terminal velocity. ft per sec (d) Compare the time it takes to reach 99% of terminal velocity here with the 25 seconds it took a skydiver with his parachute closed to reach 99% of terminal velocity in Example 2.1. On the basis of the information we have, which would you expect to reach 99% of terminal velocity first, O feather feather or a cannonball? O cannonball Need Help? Read ItA person running through the forest with equation: y(x, t) = (1.1 m)cos(3.1x – 7.1t) for which x has units of meters and t has units of seconds. Calculate the speed of the person running in m/s. Include postive or negative sign in the answer to show which direction the person is moving in
- Tom Cogwagee Longboat, of the Six Nations of the Grand River, is one of Ontario's best known distance runners. In 1907, he set a new Boston Marathon record, beating all of the previous decade's champions by almost 5 minutes! If he ran the 39.2 km course in 2 hours, 24 minutes and 24 seconds, what was his speed? HINT: we'll need our units to be metres per second - what do you need to convert in the question? 0.221 m/s O 0.272 m/s O 4.52 m/s O 17.5 m/sA car takes 5.0 s to go from v=0 m/s to v=24 m/s at constant acceleration. If you wish to find the disance traveled using the equation d=1/2at squared, what value should you use for a? Express your answer to two significant figures and includ the appropraite units.D = (oxt) + (1/2 * 8.93* (4.7)2) I D = 98.63 meter 5. You are about to skateboard down a long hill. Your initial velocity is 2.0 m/s south. When you reach the bottom of the hill you are travelling 6.0 m/s south. It took you 57 seconds to reach the bottom of the hill. What was your displacement?
- An engineer is testing how quickly a car accelerates from rest. The velocity V is measured in miles per hour, as a function of time t, in seconds, since the car is at rest. See the table below. What is the slope for the linear function modeling velocity as a function of time, V=, and what would the formula be for the velocity at time 0, V(0) Time (t) Velocity (V) 2.0 28.9 2.5 35.0 3.0 41.1 3.5 47.25. When 12 times a number is added to the square of that number, the result is ‒32. Determine the two numbers that fit this condition. Answer step-by-steps. 6. A cannonball is fired from ground level on an arc described by h = ‒t2 + 8t, where h = the height in metres and t is the time in seconds. How many seconds after firing will it land? Answer step-by-steps.The acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/s
- The acceleration of an object (in m/s) is given by the function a(t) = 7 sin(t). The initial velocity of the object is v(0) 2 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = b) Find the object's displacement (in meters) from time 0 to time 3. meters c) Find the total distance traveled by the object from time 0 to time 3. metersThe acceleration of an object (in m/s2) is given by the function a(t)=8sin(t)a(t)=8sin(t). The initial velocity of the object is v(0)=−10v(0)=-10 m/s. Round your answers to four decimal places.a) Find an equation v(t) for the object velocity.v(t)v(t) = −8cos(t)−2Correct b) Find the object's displacement (in meters) from time 0 to time 3.3.4187Incorrect metersc) Find the total distance traveled by the object from time 0 to time 3. metersGiven the quantities a = 1.4 m, b = 7.5 s, c = 86 m/s, what is the value of the quantity d = cb² Number i Units ?