Question

In: Math

A particle is moving according to the given data v(t)=t^2 - sqrt(t), x(0) = 0, 0...

A particle is moving according to the given data

v(t)=t^2 - sqrt(t), x(0) = 0, 0 ≤ t ≤ 4.

• Find x(t), the position of the particle at time t.
• For what values of t is the particle moving to the left? To the right?

• Find the displacement of the particle.
• Find the total distance covered by the particle.

Solutions

Expert Solution


Related Solutions

A particle is moving with the given data. Find the position of the particle. v(t) =...
A particle is moving with the given data. Find the position of the particle. v(t) = sin(t) − cos(t), s(0) = 4
A particle is moving with the given data. Find the position of the particle. a(t) =...
A particle is moving with the given data. Find the position of the particle. a(t) = 11 sin(t) + 3 cos(t), s(0) = 0, s(2π) = 18
The position of a particle moving along the x-axis is given by x(t) = t^3 +...
The position of a particle moving along the x-axis is given by x(t) = t^3 + 9t^2 − 21t with t is in [0, 2]. (a) Find the velocity and acceleration of the particle. (b) For what t-values is the velocity 0? (Enter your answers as a comma-separated list.) (c) When is the particle moving to the left (velocity is negative)? (Enter your answer using interval notation.) When is the particle moving to the right (velocity is positive)? (Enter your...
The velocity function of a particle moving along a line is given by the equation v(t)...
The velocity function of a particle moving along a line is given by the equation v(t) = t2 - 2t -3. The particle has initial position s(0) = 4. a. Find the displacement function b. Find the displacement traveled between t = 2 and t = 4 c. Find when the particle is moving forwards and when it moves backwards d. Find the total distance traveled between t = 2 and t = 4 e. Find the acceleration function, and...
The velocity function for a particle moving along a straight line is given by v(t) =...
The velocity function for a particle moving along a straight line is given by v(t) = 2 − 0.3t for 0 ≤ t ≤ 10, where t is in seconds and v in meters/second. The particle starts at the origin. (a) Find the position and acceleration functions for this particle. (b) After ten seconds, how far is the particle from its starting point? (c) What is the total distance travelled by the particle in the interval [0, 10]?
1. A particle is moving with the given data. Find the position of the particle. a(t)=2t+7,...
1. A particle is moving with the given data. Find the position of the particle. a(t)=2t+7, s(0)=8, v(0)=-3 2.Find f f'(x)=1 sqrt(1-x2) , f(1/2)=8
2). A particle moving on the x-axis has a time-dependent position (t) given by the equation...
2). A particle moving on the x-axis has a time-dependent position (t) given by the equation x (t) = ct - bt^3. Where the units of x are meters (m) and time t in seconds (s). (Hint: you must get derivatives, you need graph paper) (a) So that the position in x has units of meter which are the units of the constants c and b? If c = 5 and b = 1. From ti = 0s to tf...
. A particle is moving so that its velocity is v(t) = 3t 2 − 30t...
. A particle is moving so that its velocity is v(t) = 3t 2 − 30t + 48 meters/min, where t is time in minutes. a. Find the displacement (change in position) of the particle in the first 12 minutes. Give units. b. Find the total distance traveled by the particle in the first 12 minutes. Give units.
The potential of a particle is given as V (x) = -Vδ (x), with V being...
The potential of a particle is given as V (x) = -Vδ (x), with V being a positive number. Find the wave function and energy of the bounded states of this particle.
The velocity of a particle moving in the xy plane is given by ,v=(5t-4.5t^2)i+8.3j with in...
The velocity of a particle moving in the xy plane is given by ,v=(5t-4.5t^2)i+8.3j with in meters per second and t (> 0) in seconds. At t = 2.4 s and in unit-vector notation, what are (a) the x component and (b) the y component of the acceleration? (c) When (if ever) is the acceleration zero? (d) At what positive time does the speed equal 10 m/s?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT