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 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 ?
- 14 m
- 28 m
- 56 m
- 70 m
The Correct Option is C
Solution and Explanation
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
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.