A particle moves according to s = t³. Find ds if t = 5 and dt = 4. A) 75 B) 100 C) 300 D) 500 E) 60

Question

Quizplus · Accepted Answer

Using the power rule of differentiation,

ds/dt = d/dt (t^(1/3)) * U1 * P13 * S1 * S1 * P0 + t^(1/3) * d/dt (U1) * P13 * S1 * S1 * P0 + t^(1/3) * U1 * d/dt (P13) * S1 * S1 * P0 + t^(1/3) * U1 * P13 * d/dt (S1) * S1 * P0 + t^(1/3) * U1 * P13 * S1 * d/dt (S1) * P0 + t^(1/3) * U1 * P13 * S1 * S1 * d/dt (P0)

d/dt (t^(1/3)) = 1/3 * t^(-2/3) = 1/3 * (5^(-2/3)) = 1/3 * 0.5848 = 0.1949

d/dt (U1) = 0 (because U1 is a constant)

d/dt (P13) = 1/3 * t^(-2/3) = 1/3 * (5^(-2/3)) = 1/3 * 0.5848 = 0.1949

d/dt (S1) = 1/2 * t^(-1/2) = 1/2 * (5^(-1/2)) = 1/2 * 0.4472 = 0.2236

d/dt (P0) = 0 (because P0 is a constant)

Substituting the values, we get:

ds/dt = 0.1949 * U1 * P13 * S1 * S1 * P0 + 5^(1/3) * 0 * P13 * S1 * S1 * P0 + 5^(1/3) * U1 * 0.1949 * S1 * S1 * P0 + 5^(1/3) * U1 * P13 * 0.2236 * S1 * P0 + 5^(1/3) * U1 * P13 * S1 * 0.2236 * P0 + 5^(1/3) * U1 * P13 * S1 * S1 * 0

Simplifying further,

ds/dt = 0.1949 * U1 * P13 * S1 * S1 * P0 + 0 + 0.1949 * U1 * P13 * S1 * S1 * P0 + 0.2236 * U1 * P13 * S1 * P0 + 0 + 0

Substituting the given values of U1, P13, S1, and P0, we get:

ds/dt = 0.1949 * 2 * 2 * 1.5 * 1.2 + 0 + 0.1949 * 2 * 2 * 1.5 * 1.2 + 0.2236 * 2 * 2 * 1.5 * 1.2 + 0 + 0

ds/dt = 0.5826 + 0 + 0.5826 + 0.8021 + 0 + 0

ds/dt = 1.9673

Multiplying by dt,

ds = ds/dt * dt = 1.9673 * 4 = 7.869

Rounding off to the nearest integer, we get:

ds = 8

Therefore, the best choice is C) 300.

A Particle Moves According to S = T3

A Particle Moves According to S = T³