Concept explainers
(a)
The average velocity during time interval
(a)
Answer to Problem 2P
The average velocity during time interval
Explanation of Solution
Section 1:
To determine: The position vector
Answer: The position vector
Given information:
The value of
The position vector at time
Substitute
Section 2:
To determine: The position vector
Answer: The position vector
Given information:
The value of
The position vector at time
Substitute
Section 3:
To determine: The average velocity during time interval
Answer: The average velocity during time interval
Given information:
The value of
The formula to calculate average velocity is,
Substitute
Conclusion:
Therefore, the average velocity during time interval
(b)
The velocity and speed at time
(b)
Answer to Problem 2P
The velocity at time
Explanation of Solution
Section 1:
To determine: The velocity at time
Answer: The velocity at time
Given information:
The value of
The formula to calculate velocity at time
Substitute
Conclusion:
Therefore, the velocity at time
Section 2:
To determine: The speed at time
Answer: The speed at time
Given information:
The value of
The formula to calculate speed at
Calculate the magnitude of velocity as,
Conclusion:
Therefore, the speed during time interval
Want to see more full solutions like this?
Chapter 3 Solutions
Principles of Physics: A Calculus-Based Text
- Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)j, with x(t) = at + b and y(t) = ct + d, where a = 2.00 m/s, b = 1.15 m, c = 0.116 m/s2, and d = 1.08 m. (a) Calculate the average velocity during the time interval from t = 2.25 s to t= 3.80 s. m/s (b) Determine the velocity at t = 2.25 s. v = m/s Determine the speed at t = 2.25 s. m/sarrow_forwardA particle moving with an initial velocity v, = (10m/s)î and initial position 7, = (4m)î + (2m)j, undergoes an acceleration ở = 2t²î + 4ĵ in SI units. For t = 10 s; a) Calculate the velcoity v= vxI+ vy®. b) Calculate the position r= x+ y. c) What are the magnitudes of the velocity and the position vector of the particle? d) Find also the angle each vector is making with the x-axis at that time.arrow_forwardSuppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct2 + d, where a = 1.10 m/s, b = 1.25 m, c = 0.123 m/s2, and d = 1.02 m. (a) Calculate the average velocity during the time interval from t = 1.85 s to t = 3.85 s. (b) Determine the velocity and speed at t = 1.85 s.arrow_forward
- Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct² + d, where a = 1.10 m/s, b = 1.05 m, c = 0.124 m/s², and d = 1.16 m. (a) Calculate the average velocity during the time interval from t = 2.25 s to t = 3.85 s. V= (b) Determine the velocity at t = 2.25 s. V= m/s Need Help? Determine the speed at t = 2.25 s. m/s Read It m/sarrow_forwardSuppose the position vector for a particle is given as a function of time by r(t) = x(t)i + y(t)ĵ, with x(t) = at + b and y(t) = ct² +d, where a = 1.90 m/s, b = 1.50 m, c = 0.123 m/s², and d = 1.16 m. (a) Calculate the average velocity during the time interval from t = 1.90 s to t = 4.05 s. m/s V= (b) Determine the velocity at t = 1.90 s. m/s V= Determine the speed at t = 1.90 s. m/sarrow_forwardSuppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t)=ct2 + d, where a = 2.00 m/s, b = 1.35 m, c = 0.115 m/s2, and d = 1.14 m. (a) Calculate the average velocity during the time interval from t = 1.85 s to t = 3.75 s. v = m/s (b) Determine the velocity at t = 1.85 s. v = m/s Determine the speed at t = 1.85 s.arrow_forward
- Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct² + d, where a = 1.40 m/s, b = 1.50 m, c = 0.117 m/s2, and d = 1.12 m. (a) Calculate the average velocity during the time interval from t = 2.15 s to t = 4.10 s. v= 2.9i + (0.234t + 1.12)j m/s (b) Determine the velocity at t = 2.15 s. v = 2.9i + 1.57j m/s Determine the speed at t = 2.15 s. The correct answer is not zero. m/sarrow_forwardSuppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t)=ct2 + d, where a = 1.70 m/s, b = 1.20 m, c = 0.133 m/s2, and d = 1.12 m. (a) Calculate the average velocity during the time interval from t = 2.05 s to t = 3.80 s. v = m/s (b) Determine the velocity at t = 2.05 s. v = m/s (c) Determine the speed at t = 2.05 s. m/sarrow_forwardSuppose that the position vector for a particle is given as a function of time by (t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct2 + d, where a = 2.00 m/s, b = 1.05 m, c = 0.117 m/s2, and d = 1.16 m. (a) Calculate the average velocity during the time interval from t = 2.05 s to t = 3.85 s. = m/s (b) Determine the velocity at t = 2.05 s. = m/s Determine the speed at t = 2.05 s. m/sarrow_forward
- Do the first questionarrow_forwardThe acceleration vector of a particle is giving by a = -27 t2 j m/s4. The particle is located at the origin at t = 0 s and has an initial velocity Vo = 2(m/s) i + 3(m/s) j. Find: a) The velocity of the particle as a function of time. b) The maximum height the particle reaches.arrow_forwardA particle starts from the origin at t=0 with a velocity of 7.8 and moves in the xy plane with a constant acceleration of (4.4î + 3.0)) m/s² .At the instant the particle's x coordinate is 29 m, what are (a) its y coordinate and (b) its speed? (a) Number (b) Number 48 IM Units m Units m/sarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning