Question 27 (10 points) The motion of a particle moving in a horizontal direction is described by its position ( mathrm{x}(mathrm{t}) ). ( x(t)=15+6 t+6 t^{2} ) Determine the velocity, ( v(t)=d x(t) / d t ) at ( t=2 s ), and acceleration, ( a=d v(t) / d t ) at ( t=2 s ). SI units of position is in meter and time in second. ( mathrm{v}=10 mathrm{~m} / mathrm{s} ) and ( mathrm{a}=3 mathrm{~m} / mathrm{s}^{2} ) at ( mathrm{t}=2 mathrm{~s} ) ( mathrm{v}=30 mathrm{~m} / mathrm{s} ) and ( mathrm{a}=12 mathrm{~m} / mathrm{s}^{2} ) at ( mathrm{t}=2 mathrm{~s} ) ( mathrm{v}=20 mathrm{~m} / mathrm{s} ) and ( mathrm{a}=6 mathrm{~m} / mathrm{s}^{2} ) at ( mathrm{t}=2 mathrm{~s} ) ( mathrm{v}=40 mathrm{~m} / mathrm{s} ) and ( mathrm{a}=16 mathrm{~m} / mathrm{s}^{2} ) at ( mathrm{t}=2 mathrm{~s} )
Added by Emmanuel J.
Close
Step 1
x(t) = 15 + 6t + 6t^2 Taking the derivative with respect to t, we get: v(t) = dx(t)/dt = 6 + 12t Now, we need to find the velocity at t = 2s. Plugging in t = 2 into the velocity function, we get: v(2) = 6 + 12(2) = 6 + 24 = 30 m/s Show more…
Show all steps
Your feedback will help us improve your experience
Hoan Nguyen and 68 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In question 36, the position function of a particle moving along a coordinate line is given, where s is in feet and t is in seconds. a) Find the velocity and acceleration functions. b) Find the position, velocity, speed, and acceleration at time t = 1. c) At what times is the particle stopped? d) When is the particle speeding up? slowing down? e) Find the total distance traveled by the particle from time t = 0 to time t = 5. i s(t) = t^3 - 6t^2, (t >= 0) ii s(t) = t^4 - 4t + 2, (t >= 0) iii s(t) = 3 cos(pi/2 t), (0 <= t <= 5) iv s(t) = t / (t^2 + 4), (t >= 0) v s(t) = 2t^3 - 21t^2 + 60t + 3, (t >= 0)
Carson M.
The relationship between the velocity of a particle moving along the x axis and time is given by v = -3t² + 12t, where the units are SI units. At time t = 0, the particle was at position x = 20 m. The position coordinate of this particle at the turning point of its motion for time t > 0 is x = ____ 20 m 52 m 32 m 25 m
Prabhu R.
The displacement of a particle which moves along the s-axis is given by s = (-3 + 3t)e^(-0.4t), where s is in meters and t is in seconds. Plot the displacement, velocity, and acceleration versus time for the first 20 seconds of motion. Then answer the questions. When t = 3 s, s = __ m; When t = 3 s, v = __ m/s; When t = 3 s, a = __ m/s^2; The acceleration is zero when t = __ s.
Timothy J.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD