The upward velocity of a 2540kg rocket is v(t)=At + Bt2. At t=0 a=1.50m/s2. The rocket takes off and one second afterwards v=2.00m/s. Determ

Question

The upward velocity of a 2540kg rocket is v(t)=At + Bt2. At t=0 a=1.50m/s2. The rocket takes off and one second afterwards v=2.00m/s. Determine the constants A and B with units.

in progress 0
niczorrrr 5 months 2021-08-18T07:44:23+00:00 1 Answers 1 views 0

Answers ( )

    0
    2021-08-18T07:45:31+00:00

    Answer:

    The value of A is 1.5m/s^2 and B is 0.5m/s^³

    Explanation:

    The mass of the rocket = 2540 kg.

    Given velocity, v(t)=At + Bt^2

    Given t =0  

    a= 1.50 m/s^2

    Now, velocity V(t) = A*t + B*t²

    If,  V(0) = 0, V(1) = 2

    a(t) = dV/dt = A+2B × t  

    a(0) = 1.5m/s^²  

    1.5m/s^²  =  A + 2B ×  0  

    A = 1.5m/s^2


    now,

    V(1) = 2 = A× 1 + B× 1^²  

    1.5× 1 +B× 1 = 2m/s

    B = 2-1.5  

    B = 0.5m/s^³


    Now Check V(t) = A× t + B × t^²

    So, V(1) = A× (1s) + B× (1s)^² = 1.5m/s^² ×  1s + 0.5m/s^³ × (1s)^² = 1.5m/s + 0.5m/s = 2m/s  

    Therefore, B is having a unit of m/s^³ so B× (1s)^² has units of velocity (m/s)

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )