Given the equation vf = Vị + a*t , and multiple measurements of final velocity and time, which variable should you plot on the y-axis if you want the acceleration to be given by the slope of the curve?
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- Over a time interval of 1.52 years, the velocity of a planet orbiting a distant star reverses direction, changing from +20.5 km/s to -15.8 km/s. Find (a) the total change in the planet's velocity (in m/s) and (b) its average acceleration (in m/s2) during this interval. Include the correct algebraic sign with your answers to convey the directions of the velocity and the acceleration. (a) Number i -3775.2 (b) Number i -7.58 Units Units m/s m/s^2Scenario: A toy rocket is launched straight upward from a pad 10 ft above ground level with an initial velocity of 80 ft/sec. Use the general formula for the vertical position (height) of an object moving under the influence of gravity where s0 is the initial vertical position, v0 is the initial velocity, and s is the vertical position of the object. Graph your equation with time on the horizontal axis and height on the vertical axis. Let the values for the time range from 0 to 10 seconds and the values for the height range from 0 to 200 feet. Include your graph in this response.An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s?
- You 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?A cork bobs up and down in a lake. The distance from the bottom of the lake to the center of the cork at time t>=0 is given by s(t)= 25+cos(pi t), where s(t) is in feet and t Is in seconds. During what time interval is the cork rising. Draw pictures as wellAn object is travelling in 1-dimension (i.e. along the x- axis) with a velocity described by the equation: v(t)=v0+1/6st^3 , where s and v0 are constants. The object’s position, and acceleration at time t = 0 are given by d0, and a0 respectively. In terms of the variables given, what is the average acceleration of the object over the interval from 0 to 2 seconds.
- A particle moving along the x axis has acceleration in the x direction as function of the time given by a(t) = 6t²-t. For t=0 the initial velocity is 6.0 m/s. Determine the velocity when t = 1.0 s. Write here your answer. Include the units.A particle moves so that its position (in meters) as a function of time (in seconds) is r = î + 5t2 j + 5t k. (Use the following as necessary: t.) (a) Write an expression for its velocity as a function of time. V = m/s (b) Write an expression for its acceleration as a function of time. a = m/s?An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s? with everything in 3 sig figs
- I don't understand how to do this problem. I tried taking the derivative, but that didn't give me the correct answer. I would really appreciate the help. When a 1984 Alpha Romeo Spider sports car accelerates in the x-direction at the maximum possible rate,its motion during the first 20. seconds is extremely well modeled by the simple equation vx2=(60 m2/s3)t, where t is time in seconds and vx is in m/s. In other words, the squareof teh car's velocity increases linearly with time. What is its acceleration after 3s, assuming that the car starts from rest at t=0 s?Needs Complete solution with 100 % accuracy. don't use chat gpt or ai plz. I definitely upvote you.Solve the last part