The velocity of a rocket in space is given by v(t) = A ln(1 + Bt)...
an objects velocity as a function of time is given by v(t)=bt-ct^3, where b and c are positive constants with appropriate units. if the object starts at x=0 at the time t=0, find expressions for a) the time when its again at x=0 and b) its acceleration at that time.
The acceleration of a certain rocket is given by ax= bt, where b is a positive constant. (a) Find the position function x(t) if x = x0 and v0 at t = 0. (Use the following as necessary: x0, v0, b, and t.) x(t) = (b) Find the position and velocity at t = 7.9 s if x0 = 0, v0 = 0 and b = 3.3 m/s3. x(7.9 s) = m v(7.9 s) = m/s (c) Compute the average velocity of...
A rocket with an initial velocity vo turns on its boosters so that its acceleration becomes a(t)= p2t2-k2, where k and p are positive constants with appropriate units. Find an expression for the maximum velocity of the rocket after t = 0.
A rocket is fired at an angle from the top of a tower of height h0 = 40.0 m. Because of the design of the engines, its position coordinates are of the form x(t) = A + B t2 and y(t) = C + D t3, where A, B, C and D are constants. The acceleration of the rocket 3.00 s after firing is a = (7.00 i + 5.00 j) m/s2. Take the origin of coordinates to be at...
QB: The Rocket Equation The velocity of a rocket t seconds after liftoff from earth can be modeled by v(t) = -g*t - v_e * Ln( (m-r*t)/m ) where g = 9.8 m/s^2, the usual earth gravity value, v_e = exhaust velocity, 3000 m/s (the e here isn't related to 2.71828...) m = initial mass of the rocket+fuel: 30,000 kg r = rate of using fuel = 160 kg/s i) Find a formula for the acceleration function a(t) and graph...
vProblem: A possible model for a sprinter's velocity is given by Vx=a(1-e^(-bt))where t is in seconds, vx is in m/s, and the constants a and b are characteristic of the sprinter. Assume Sprinter A runs the 100-meter dash following this prescription with a = 11.81 m/s and b = 0.6887 s-1. a) Find an expression for Sprinter A’s acceleration as a function of time t. b) Find an expression for the distance traveled by Sprinter A as w.r.t. time t....
2.53 CALC The acceleration of a motorcycle is given by az(t) = At - Bt?, where A = 1.50 m/s and B = 0.120 m/s4. The motorcycle is at rest at the origin at time t = 0. (a) Find its position and velocity as functions of time (b) Calculate the maxi- mum velocity it attains.
4. The position of an object as a function of time is given by x(t) at-bt ct-d, where a 3.6 m/s, b 4 m/s, c = 60 m/s and d= 7 m. (a) Find the instantaneous velocity at t =24 s. (b) Find the average velocity over the first 2.4 seconds, (c) Find the instantaneous acceleration at 2.4 s, (d) Find the average acceleration over the first 2.4 seconds. (Be sure to include the correct signs) (a) and (c) are...
4. The velocity of rocket initially at the origin is v = [0.8571+ (4.0-0.60r ) ]m/ stins Th coordinate is "up" a) Find and the magnitude and direction of the acceleration à (1). b) Find the position r(t) as a function of time. c) Using the velocity, find the time it reaches velocity, find the time it reaches its maximum height, then evaluate that height
An object's motion is represented by the x vs. t graph shown below Hint: Velocity is the slope of x vs. t graph, and acceleration is slope of v vs. t graph. 130 points: 5 points each r (s) t (a) a. Draw the corresponding v vs. t graph on the axes provided. b. Draw the corresponding a vs. t graph on the axes provided. c. At what times is the position a maximum (most positive)? At those times, is...