Solution Found!
The acceleration of a bus is given by ax(t) = ?t, where ?
Chapter 2, Problem 52E(choose chapter or problem)
Problem 52E
The acceleration of a bus is given by ax(t) = αt, where α = 1.2 m/s3. (a) If the bus’s velocity at time t = 1.0 s is 5.0 m/s, what is its velocity at time t = 2.0 s? (b) If the bus’s position at time t = 1.0 s is 6.0 m, what is its position at time t = 2.0 s? (c) Sketch ax-t, vx-t, and x-t graphs for the motion.
Questions & Answers
QUESTION:
Problem 52E
The acceleration of a bus is given by ax(t) = αt, where α = 1.2 m/s3. (a) If the bus’s velocity at time t = 1.0 s is 5.0 m/s, what is its velocity at time t = 2.0 s? (b) If the bus’s position at time t = 1.0 s is 6.0 m, what is its position at time t = 2.0 s? (c) Sketch ax-t, vx-t, and x-t graphs for the motion.
ANSWER:
Solution 52E
(a) The acceleration is given by
….(1)
We can get the velocity of the particle by integrating the above equation with respect to . So integrating the above equation with respect to
, we have
Where C is the constant of integration and can be calculated from the initial condition.
Now the initial condition for velocity is at t=1.0 s, . Using the above condition we have
