Position velocity acceleration
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- The position of a particle moving along a straight line is given by:
where t is measured in seconds and s in meters.
- Find the position of the particle at: t=0,1,2,3,4,5,6,7, and draw a diagram to illustrate the positions of the particle.
- Find the velocity at time t.
- Find the velocity of the particle at: t=1,3,5,7.
- When is the particle: i) at rest? ii) moving forward (that is, moving in the positive direction)? iii) moving backward (that is, moving in the negative direction)? Draw a diagram to illustrate the motion of the particle.
- Find the total distance traveled by the particle during the first 7 seconds.
- Find the acceleration at time t.
- Compare the velocity and acceleration of the particle at: t=1,3,5,7, and determine whether the particle is speeding up or slowing down at each instant.
- Graph the position, velocity, and acceleration functions for
- When is the particle: i) speeding up? ii) slowing down?