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.

Answer 1

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

Step-by-step 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)