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 ?

• A. 14 m
• B. 28 m
• C. 56 m
• D. 70 m

Answer 1

Answer: (C)

56 m

Answer 2

Particle Coming to Rest: To find when the particle comes to rest, we need to find the time at which the velocity becomes zero.
The velocity function is given as v = 40 + 12t - t3.
Set v = 0 : 0 = 40 + 12t - t3.
Solving this equation for t, we find t = 4 seconds.
To find the distance traveled before coming to rest, use the equation for displacement:
x = $\int$(0 to 4) v $dt$.
Calculating the integral, and we find that the particle travels a distance of 56 meters.

Therefore, the correct option is (C): 56 m