Question 1: A snowboarder starts from rest at the top of a double black diamond hill. As she rides down the slope, GPS coordinates are used to determine her displacement as a function of time given by the image below, where x and t are expressed in feet and seconds, respectively. Determine the position, velocity, and acceleration of the boarder when t=5 seconds. Write your answer in the format (x= ft ;v = - ft/s ; a = ft/s^2) X = 0.5t3 + t2 + 2t Your answer

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?

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?

Pls help ASAP

Pls help ASAP

A particle moves so that its position (in meters) as a function of time (in seconds) is r = î + 2t² j+ 2tk. (Use the following as necessary: t.) (a) Write an expression for its velocity as a function of time. v(t) = m/s (b) Write an expression for its acceleration as a function of time. d(t) = m/s2 Submit Answer

1. A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 610 mi/h, how far is she from her starting position?Your answer is    mi;Enter your answer rounded to two decimal places.   2. A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 880 ft out in the plain from the base of the mountain. Find the shortest length of cable needed.Your answer is    ft

At what initial speed must the basketball player throw the ball at angle θ0 = 66° to make the foul shot.  d1=1.0 ft, d2=14.0 ft, h1= 7.0 ft and h2= 10 ft.  Enter units in ft/s.  Use g = 32 ft/s/s.  Compute your answer to the ±0.1 f/s.  Hint: Use x = tvcos(θ) and y=vsin(θ)t - 1/2gt2

Please answers parts a and b

The prompt is in the image attached. The questions I need help are:a) Evaluate the acceleration at t=1.0 s. Express your answer in m/s^2 in 2 significant figures.b) Evaluate the acceleration at t=11s. Express your answer in m/s^2 in 2 significant figures.Thank you!