A 3kg particle moves along the X axis according to X(t) = 6t+3t2+2t3, where X is...

A 3kg particle moves along the X axis according to X(t) = 6t+3t²+2t³, where X is in meters and t is in seconds. What net force is acting on it at t = 3 s?

Solutions

Expert Solution

We have the position of the particle varies with the time according to the equation as,

On differentiating the postion with respect to time,we get the velocity at time t,

ie,

On differentiating the velocity with respect to the time,we get the instantaneous acceleration for time t,

So,The instantaneous acceleration of the particle at time t, is given by,

By Newtons 2nd law of motion,we have,

The net unbalanced force acting on the particle,

We have the mass of the particle is,

at time the acceleration of the particle,

So,The instantaneous acceleration at time is,

So,The net force on the body at is,

ie,

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A 0.150 kg particle moves along an x axis according to x(t) = −13.00 + 2.00t...

A 0.150 kg particle moves along an x axis according to x(t) = −13.00 + 2.00t + 3.50t2 − 2.50t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.55 s? F with arrow = ______ N

An object moves along the x-axis according to the equation x = 3t ^ 3 - 2t ^ 2 + t along the x-axis.

An object moves along the x-axis according to the equation x = 3t ^ 3 - 2t ^ 2 + t along the x-axis. Find the instantaneous velocity at t = 2 s.A) 29 B) 18 C) 48 D) 43

Consider a 2.0-kgkg object that moves along the x axis according to the expression x(t)=ct3x(t)=ct3, where...

Consider a 2.0-kgkg object that moves along the x axis according to the expression x(t)=ct3x(t)=ct3, where cc = +0.230 m/s3m/s3 . Determine the xx component of the object's average velocity during the interval from titi = 0.500 ss to tftf = 1.50 ss. Use all significant digits provided by your calculator? Repeat for the interval from titi = 0.950 ss to tftf = 1.05 ss. Use all significant digits provided by your calculator? Repeat for the interval from titi =...

Suppose a particle moves along a line according to the motion function f(t) = 9/t+9, where...

Suppose a particle moves along a line according to the motion function f(t) = 9/t+9, where t is measured in seconds and f(t) is measured in feet. Use this motion function to answer the following questions: a.) What is the initial velocity of the particle? b.) When is the particle at rest? c.) When is the particle moving in the negative direction?

Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to...

Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to the left or right with equal probability. a)What is the pdf of its position after three steps? b)What is the pdf of its position after three steps if the x-axis beginning at 1? c)What is the pdf of its position after two steps? d)What is the pdf of its position after two steps if the x-axis beginning at 1?

A particle moves along the x axis. It is initially at the position 0.250 m, moving...

A particle moves along the x axis. It is initially at the position 0.250 m, moving with velocity 0.070 m/s and acceleration -0.250 m/s2. Suppose it moves with constant acceleration for 3.90 s. Assume it moves with simple harmonic motion for 3.90 s and x = 0 is its equilibrium position. (a) Find its position. (b) Find its velocity at the end of this time interval.

A particle moves along the x axis. It is initially at the position 0.200 m, moving...

A particle moves along the x axis. It is initially at the position 0.200 m, moving with velocity 0.140 m/s and acceleration -0.410 m/s2. Suppose it moves with constant acceleration for 5.50 s. We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 5.50 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you...

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 position of a particle moving along the x axis depends on the time according to...

The position of a particle moving along the x axis depends on the time according to the equation x = ct2 - bt3, where x is in meters and t in seconds. For the following, let the numerical values of a and b be 3.7 and 1.0 respectively. a) At what time does the particle reach its maximum positive x position? b) What distance does the particle cover in the first 4.0s? c) What is its displacement from t=0s to...

1D Kinematics Problem: An object moves along the x axis according to the equation x =...

1D Kinematics Problem: An object moves along the x axis according to the equation x = 2.80t2 − 2.00t + 3.00, where x is in meters and t is in seconds. (a) Determine the average speed between t = 2.10 s and t = 3.40 s. (b) Determine the instantaneous speed at t = 2.10 s. Determine the instantaneous speed at t = 3.40 s. (c) Determine the average acceleration between t = 2.10 s and t = 3.40 s....

Subjects