A 5 kilogram sphere is moving in the XY plane accordinng to the following equati

Question

A 5 kilogram sphere is moving in the XY plane accordinng to the following equations. Find the following parameter when t = 2 seconds: (a) at what radial distance is the sphere from the origin? (b) What is the magnitude of the velocity in m/s? (c) What is the magnitude of acceleration in m/square seconds? (d) What is the magnitude of the force acting on the sphere in Newton? All answers mu st have the proper units X = 10t + 0. 5 t2 y =60 t2 - 10t z = 20t Note: Distances are in meters, singles in radians and time in seconds. g = 980. 1 meters per square seconds.

Explanation / Answer

This must be a physics question because: x = 10t + .5t^2 is position y = 60t^2 - 10t is the derivative of position which is velocity z = 20t is the derivative of velocity which is acceleration so when your finding: a.) The radial DISTANCE, you must use position equation (just plug in time) your time given is 2 seconds x = 10(2) + .5(2)^2 = 18 meters b.) when it ask for a magnitude it means it doesn't want a direction and direction can be negative and magnitudes are always positive! so y= 60(2)^2 - 10(2) = 220 m/s c.) z= 20(2) = 40 m/s^2 d.) Force = mass times acceleration due to gravity g is usually 9.81 m/s^2 but they give it to be 980.1 meters per second per second so F= (5kg)(980.1 m/s^2) = 4900.5 kg*m/s^2 where 1 Newton = 1 kg*m/s^2 =4900.5 N Please rate me to let me know how I did! I hope this helped!!

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