Question

The position of a particle moving along the x axis is given in centimeters by x = 9.45 + 1.77 t3, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t = 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s.

Answer 1

Answer: a) 34.45 m/s; b) 21.24 m/s; c) 47.79; d) 33.18 m/s ; e) 35.62 m/s

Explanation: We have to use the expression x = 9.45 + 1.77 t3, where t is in seconds. From the we can obtain the expression for the velocity by deriving this. So you can replace the values the time to calculate the instant velocity and  then determine the average velocity for t=2s and t=3 s adding both values a dividing by 2.

Finally to find the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s., you have to obtain the distance for this value and get the middle positions and then find the time to reach this point. With this time value and by using the instant velocity expression you can determine v  for this time.