he displacement of a particle is givenby 𝑥 = (𝑡 − 2)2 where x is in meters andt in seconds. The distance covered bythe particle in first 4 seconds is
Question
he displacement of a particle is givenby 𝑥 = (𝑡 − 2)2 where x is in meters andt in seconds. The distance covered bythe particle in first 4 seconds is
Solution
The displacement of a particle is given by the equation 𝑥 = (𝑡 − 2)². This is a parabolic equation, which means the particle moves in a parabolic path.
Step 1: Find the displacement at t=0s and t=4s.
At t=0s, x = (0-2)² = 4 meters (to the left of the origin, assuming right is positive) At t=4s, x = (4-2)² = 4 meters (to the right of the origin)
Step 2: Calculate the total distance covered.
The particle moves 4 meters to the left, then 4 meters to the right. So, the total distance covered by the particle in the first 4 seconds is 4m (left) + 4m (right) = 8 meters.
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