The vector position of a particle varies in time according to the expression  = 3.80 î − 8.80t2 ĵ where  is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.)   =       m/s (b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.)   =       m/s2 (c) Calculate the particle's position and velocity at t = 5.00 s.   =       m   =       m/s

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I need help with this practice problem. I was given the answer key but I need help solving it step by step.  A car drives North for 1 km. Then it turns and drives 2 km at 30◦ South of West.Finally the driver turns again and drives 0.5 km Northwest.(a) What is the total distance driven?(b) What are the magnitude and direction of the car’s overall displacement? Answer Key: a.) 3.5 km b.) .11 km, 9.55◦

A rocket's position (in meters) as a function of time (in seconds) is given below. Round all answers in this problem to one decimal place r² = (t² − 3t)i + (t³ + 3)ĵ (a) What is the magnitude of the rocket's (in m/s) velocity at t = 2.5 s? (b) In what direction is the rocket moving (in degrees) at t = 2.5 s? (c) What is the magnitude of the rocket's acceleration (in m/s²) at t = 2.5 s?

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

The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a person's bank account balance. The units of x would be dollars ($) and velocity v would give the rate at which the balance changes (in units of, for example, $/month). Acceleration would give the rate at which v changes. Suppose a person begins with one hundred dollars in the bank. Initial money management leads to no net change in the account balance so that  v0 = 0.  Unfortunately, management worsens over time so that  a = −3.82 ✕ 102 $/month2.  Assuming a is constant, find the amount of time in months until the bank account is empty.    ?months

A bird flies 3.50 km [East] and then immediately turns around and flies 7.50 km [West]. The bird's average speed for the entire motion is 11.0 km/h. What is the bird's average velocity. Give your answer in km/h to 2 decimal places. A velocity that is west should be treated as negative and a negative sign should be included in your answer. A velocity that is east should be treated as positive but no sign should be included in the answer. Do not include units in your answer.