Ask Question
10 June, 21:33

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by (a) What are and, the x - and y-components of the velocity of the car as functions of time? (b) What are the magnitude and direction of the velocity of the car at? (b) What are the magnitude and direction of the acceleration of the car at? calculus based

+5
Answers (1)
  1. 10 June, 22:37
    0
    a) ax = (-0.036a) t m/s^3; ay = 0.55 m/s^2

    b) |v| = 7.469 m/s; Θ = 59°

    c) |a| = 0.62 m/s^2; Θ = 298°

    Explanation:

    a)

    the instantaneous acceleration equation will be equal to:

    a = dv/dt

    ax (t) = (d * (5-0.018*t^2)) / dt = - 0.036*t

    ay (t) = (d * (2+0.55*t)) / dt = 0.55

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

    b)

    at a time of 8 seconds, the speed of the vector will be equal to:

    v = (5 - 0.018*8^2) i + (2 + 0.55*8) j = 3.85i + 6.4j

    the magnitude of the vector will be equal to:

    |v| = (vx^2 + vy^2) ^1/2 = (3.85^2 + 6.4^2) ^1/2 = 7.469 m/s

    the direction of the vector is equal to:

    Θ = tan-1 (vy/vx) = tan-1 (6.4/3.85) = 59°

    c)

    the vector acceleration at a time of 8 seconds will be equal to:

    a = (-0.036*8) i + 0.55j = - 0.288i + 0.55j

    the magnitude will be equal to:

    |a| = (ax^2 + ay^2) ^1/2 = ((-0.288^2) + 0.55^2) ^1/2 = 0.62 m/s^2

    the direction:

    Θ = tan-1 (ay/ax) = tan-1 (0.55/-0.288) = 298°
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 (a) What are and, the ...” in 📘 Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers