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^.

1.) What is the magnitude of the velocity of the car at t = 7.78 s ?

2.) What is the direction (in degrees counterclockwise from +x-axis) of the velocity of the car at t = 7.78 s ?

3.) What is the magnitude of the acceleration of the car at t = 7.78 s ?

4.) What is the direction (in degrees counterclockwise from +x-axis) of the acceleration of the car at t = 7.78 s ?

Explanation / Answer

here,

u = ( 5 - 0.018 t^2 ) i + ( 2 + 0.55 t ) j ...(1)

1)

at t = 7.78 s

u = ( 5 - 0.018 7.78^2 ) i + ( 2 + 0.55 * 7.78 ) j

u = (3.91 i + 6.279 j) m/s

magnitude , |u| = sqrt(3.91^2 + 6.279^2) = 7.4 m/s

2)

theta = arctan(6.279 /3.91) = 58.1 degree

the direction is 58.1 degree counterclockwise from +x axis

3)

differentiating the equation (1) for a

a = ( - 0.036 t ) i + (0.55) j

at t = 7.78 s

a = ( - 0.28 ) i + (0.55) j m/s^2

|a| = sqrt(0.28^2 + 0.55^2) = 0.62 m/s^2

4)

theta' = arctan(0.55/0.28) = 116.98 degree counterclockwise from +x axis

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