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 - $t^2$. How long would the particle travel before coming to rest for a moment?

• A. 24 m
• B. 40 m
• C. 56 m
• D. 16 m

Answer 1

The calculated distance traveled is 36 m. Since this is not an option, there might be an error in the question or options. If we assume a typo in the question, where the term was $8t$ instead of $12t$, then the answer would be 16m (Option D). However, based on the question as given, 36m is the correct calculation.

Answer 2

1. Find velocity $v = \frac{dX}{dt} = 12 - 2t$.

2. Set $v=0$ to find time to rest: $12 - 2t = 0 \implies t = 6$ s.

3. Calculate initial position $X(0) = 40$ m.

4. Calculate position at rest $X(6) = 40 + 12(6) - (6)^2 = 76$ m.

5. Distance traveled = $|X(6) - X(0)| = |76 - 40| = 36$ m.

The calculated answer (36 m) is not among the options.