A remote-controlled car is moving in a vacant parking lot. The velocity of the c

Question

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by =[5.00m/s(0.0180m/s3)t2]i^ + [2.00m/s+(0.550m/s2)t]j^

A.What is the magnitude of the velocity of the car at t = 7.90 s ?

B. What is the direction (in degrees counterclockwise from +x-axis) of the velocity of the car at t = 7.90 s ?

C. What is the magnitude of the acceleration of the car at t = 7.90 s ?

D. What is the direction (in degrees counterclockwise from +x-axis) of the acceleration of the car at t = 7.90 s ?

Explanation / Answer

here,

u = ( 5 - 0.018 t^2) i + ( 2 + 0.55 * t) j m/s

a)

at t = 7.9 s

u = ( 5 - 0.018 * 7.9^2) i + ( 2 + 0.55 * 7.9) j m/s

u = ( 3.88 i + 6.35 j) m/s

the magnitiude of velocity , |u| = sqrt(3.88^2 + 6.35^2)

|u| = 7.44 m/s

b)

the direction , theta = arctan(6.35/3.88) = 58.6 degree counterclockwise from +x axis

c)

differentiating the equation of velocity for a

a = ( - 0.036 t) i + ( 0.55 ) j m/s^2

at t = 7.9 s

the magnitude of accelration , a = sqrt(0.036^2 + 0.55^2)

a = 0.55 m/s^2

d)

phi = arctan(0.55/0.036)

phi = 93.7 degree counter clockwise from +x axis

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