Solve please (2 points) Suppose that the equation of motion for a particle (where s is...
Suppose that the equation of motion for a particle (where ss is in meters and tt in seconds) is: s=(1/3)t^3−3t^2+9t+7 Velocity at time tt = Acceleration at time tt = Acceleration after 1 second: acceleration at the instant when the velocity is 0.
Use Python to solve each problem. 2. A particle moves according to a law of motion s = t 3 − 12t 2 + 24t, t ≥ 0. a) Find the velocity at time t. b) What is the velocity after 1 second? c) When is the particle at rest? d) Sketch the position function on t ∈ [0, 6] to determine when the particle is moving in the positive direction on that interval. e) Find the total distance traveled...
Need both answered please! 1. A particle moves with acceleration function a(t) = 8t + 5. Its initial velocity is v(O) = -4 cm/s and its initial displacement is s(0) = 5. Find its position after t seconds. s 2. The equation of motion of a particle is S = t3 - 9t, where s in meters, and t is in seconds. Find a) The velocity and acceleration as a function oft b) The acceleration after 4 seconds.
Not sure if these are right 2· The e motion of a particle is modelled by the equation s(e) 5+9t-6t2+t3, where s is measured in metres and t is time in seconds. a) When is the particle at rest? (2) (3) When is the particle moving in a positive direction? b) vct) -124+30 Ct-1 Ct d-9-12t t3t2 ve) c) Draw a diagram to show the motion of the particle with respect to a distance axis, Indicate key time values Determine...
A particle moves along the x axis according to the equation x = 1.91 2.99t-1.00e, where x is in meters and t is in seconds. (a) Find the position of the particle at t 2.90 s (b) Find its velocity at t- 2.90 s m/s (c) Find its acceleration at t 2.90s m/s? My Note (a) Can the velocity of an object at an instant of time be greater in magnitude than the average velocity over a time interval containing...
A particle moves according to a law of motion s = ft), t 0, where t is measured in seconds and s in feet. t)-te-t2 (a) Find the velocity at time t (in ft/s) v(t) e (b) What is the velocity after 2 s? (Round your answer to two decimal places.) v(2) ft/s (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total...
The acceleration of a particle is given by a = 7t-14, where a is in meters per second squared and t is in seconds. Determine the velocity and displacement as functions of time. The initial displacement at t-0 is S0 -4 m, and the initial velocity is Vo 6 m/s. Once you have determined the functions of time, answer the questions Questions: when t = 5.8 s, v= m/s m/s?
3.) The position of a particle is given by x(t) = 3t3 – 2t2 – 5t + 10, where t is in seconds and x is in meters. Find the initial position of the particle. Find the position of the particle after 5 seconds. Find the average velocity from 0 sec to t = 5sec Find the instantaneous velocity as a function of time Find the instantaneous velocity at t = 2 seconds. Find the instantaneous velocity at t=4 seconds...
14. x Find the derivative of the function using the definition f(x) = x + 3 15. The equation of motion of a particle is s = p - 27t, where s is in meters and t is in seconds. (Assume 10.) (a) Find the velocity and acceleration as functions of t. (b) Find the acceleration after 4 s. (c) (c) Find the acceleration when the velocity is 0. 16. Find the points on the curve y = 2x3 +...
2. (8 points) Suppose a particle is moving in a straight line with velocity v(t) = (x + 1)2 – 2 meters per second, with an initial position s(0) = 8 meters. Find the total distance traveled by the particle after 9 seconds. Round to the nearest hundredth.