OnlineCBT
Physics · MOTION IN A STRAIGHT LINE
हिन्दीThe position \( x \) of a particle moving along a straight line varies with time \( t \) according to \( x(t) = 2t^3 - 9t^2 + 12t + 5 \) (where \( x \) is in meters and \( t \) is in seconds). The total distance traveled by the particle from \( t = 0 \) to \( t = 3\text{ s} \) is:
Correct answer · Option 1
\( 11\text{ m} \)
Explanation
Velocity \( v = \frac{dx}{dt} = 6(t-1)(t-2) \). Turning points are \( t=1\text{ s} \) and \( t=2\text{ s} \). Positions: \( x(0)=5\text{ m} \), \( x(1)=10\text{ m} \), \( x(2)=9\text{ m} \), \( x(3)=14\text{ m} \). Total distance = \( |10-5| + |9-10| + |14-9| = 5 + 1 + 5 = 11\text{ m} \).
