the motion of a particle moving in a straight line is described by x=3 cos2t, where the symbol have their usual meaning determine the distance x , where the speed is zero

Question

Answer

Solution:

Distance where the speed is zero

The motion of a particle moving in a straight line is given by the equation x = 3cos2t, where x denotes the distance of the particle from a fixed point and t denotes the time elapsed.

The speed of the particle is given by the derivative of x with respect to time t.

v = dx/dt = -6sin2t

To find the distance where the speed is zero, we need to find the values of t for which v = 0.

-6sin2t = 0

sin2t = 0

2t = nπ, where n is an integer

t = nπ/2, where n is an integer

Substituting the values of t in the equation x = 3cos2t, we get:

x = 3cos(nπ)

For even values of n, cos(nπ) = 1

For odd values of n, cos(nπ) = -1

Therefore, the distance x where the speed of the particle is zero is given by:

x = 3 for even values of n

x = -3 for odd values of n

Thus, the distance where the speed is zero alternates between 3 and -3 as the particle moves along the straight line.

Therefore, the distance x where the speed is zero is given by the equation:

x = 3n, where n is an even integer

x = -3n, where n is an odd integer.

Answer

Similar Class 12 Doubts

The distance s of a particle moving along a straight line from a fixed-pointO on the line at time t seconds after start is given by x = (t – 1)2(t – 2)2. What will be the distance of the particle from O when its velocity is zero?

The displacement of a particle moving in a straight line is described by the relation, s =6 + 12t -2(t squar e) . here s is in metre and t is in second. the distance covered by particle in first 5 sec is (

A particle moves with uniform acceleration along a straight line and describes distances 21m, 43m and 91m at times 2, 4 and 7 seconds,respectively.What is the distance described by the particle in 3 seconds?

Displacement of a particle moving on a straight line is given by x=16t-2t2. Distance travelled by the particle during the first 2sec. isS1 and during first 6sec . is S2 find 3S1/S2?

Top Courses for Class 12

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams