A particle moves along a straight line OX. At a time t (in seconds), the distance x (in metres) of the particle from O is given by x = 40 + 12t - t³. How long would the particle travel before coming to rest?
Options

Question

A particle moves along a straight line OX. At a time t (in seconds), the distance x (in metres) of the particle from O is given by x = 40 + 12t - t³. How long would the particle travel before coming to rest?

Options

G1 Physics · Accepted Answer

Step 1: v = dx/dt = 12 − 3t². Step 2: At the instant it comes to rest, v = 0, so 12 − 3t² = 0 and t = 2 s. Step 3: Distance travelled from t=0 to 2 s is ∫₀²(12−3t²)dt = [12t−t³]₀² = 24−8 = 16 m. Final answer: A.

A particle moves along a straight line OX. At a time t (in seconds), the distance x (in metres) of the particle from O is given by x = 40 + 12t − t³. How long would the particle travel before coming to rest?