Question

If the displacement of a particle at time t is given by S = 2t³ – 5t² + 4t – 3, then its acceleration at time t = 1 is ______.

विकल्प

• 2

• 8

• 10

• 14

Answer 1

If the displacement of a particle at time t is given by S = 2t³ – 5t² + 4t – 3, then its acceleration at time t = 1 is 2.

Explanation:

Given displacement:

S = 2t³ – 5t² + 4t – 3

Step 1: Find velocity (First derivative)

v = `(dS)/(dt) = d/dt(2t^3 – 5t^2 + 4t - 3)`

v = 6t² – 10t + 4

Step 2: Find acceleration (Second derivative)

a = `(dv)/(dt) = d/dt (6t^2 - 10t + 4)`

a = 12t – 10

Step 3: Find acceleration at t = 1

a = 12(1) – 10

a = 12 – 10

a = 2