the displacement of a particles is given by S=A+Bt+Ct^2.deduce the values of the constant A,B,and C appearing in the equation
A length
B length/time or velocity
C length/time^2 or acceleration
Doorh!
The displacement of a particle is given by s=a+bt+ct^2 deduce the value of the constant a,b and c
S=a+bt+ct^2. We have that s=lt^-1 and a=m or l or t b=m or l or t c=m or l or t
Suppose the displacement of a partical isvrelate to time accordoing to expressions S=ct2.what are the dimensins of the constant c.
To deduce the values of the constants A, B, and C appearing in the equation S = A + Bt + Ct^2, we need some additional information. Specifically, we require the initial displacement, velocity, and acceleration of the particle at a given time.
The equation S = A + Bt + Ct^2 represents the motion of the particle with respect to time. Each term in the equation represents a different factor affecting the displacement.
To find the values of A, B, and C, we can use the initial conditions, such as the initial displacement, velocity, or acceleration.
1. If you have the initial displacement (S₀), you can substitute the initial time (t₀ = 0) into the equation to get:
S₀ = A + B(0) + C(0)^2
S₀ = A
Therefore, the value of A is equal to the initial displacement (S₀).
2. If you have the initial velocity (V₀), you can differentiate the equation with respect to time (t) to find the velocity equation:
V = dS/dt = d/dt (A + Bt + Ct^2)
V = B + 2Ct
By substituting the initial time (t₀ = 0) and initial velocity (V₀), you can solve for B:
V₀ = B + 2C(0)
V₀ = B
Hence, B is equal to the initial velocity (V₀).
3. If you have the initial acceleration (a₀), you can differentiate the velocity equation with respect to time to find the acceleration equation:
a = dV/dt = d/dt (B + 2Ct)
a = 2C
By substituting the initial time (t₀ = 0) and initial acceleration (a₀), you can solve for C:
a₀ = 2C
Therefore, C is equal to half of the initial acceleration (a₀) because the coefficient in front of t^2 is 2C.
In summary, the values of the constants in the equation S = A + Bt + Ct^2 are:
- A: Initial displacement (S₀)
- B: Initial velocity (V₀)
- C: Half of the initial acceleration (a₀/2)