Question

A particle moves along a straight line OX. At a time t(in seconds) the distance x(in meters)of the particle from 0 is given by:-x=40+12t−t³. How long would the particles travel before coming to rest? a. 16m b. 24m c. 40m d. 56m

Answer 1

The particle comes to rest after traveling 56 meters along the line OX. This is derived from the given function representing the particle's distance from 0 along the line OX as a function of time.

The answer is d. 56m.

Step-by-step explanation:

The problem provided pertains to the motion of a particle along a straight line in physics. The distance x at time t is given by the equation x = 40 + 12t - t³. To find when the particle comes to rest, we need to solve for t when the velocity, which is the derivative of the given function, is equal to zero.

The derivative of x with respect to t gives us the velocity v = 12 - 3t². Therefore, by equating v = 0, we get t² = 4, which implies t = ±2 seconds. However, time can't be negative, so t = 2 seconds.

Then, we can plug t = 2 back into the original equation to find the distance. This gives us x = 40 + 12*2 - (2)³ = 40 + 24 - 8 = 56 meters. Hence, the particle travels 56m before coming to rest.

So, the answer is d. 56m.

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