At t = 0, an object starts with an initial velocity of -10 m/s from an initial p
ID: 1524894 • Letter: A
Question
At t = 0, an object starts with an initial velocity of -10 m/s from an initial position coordinate, x = 15 m, and moves along the x-axis with an acceleration given as: a_x = 2t - 3, in m/s^2 with t in s. What is the instantaneous velocity of the object at t = 1 s Compute the average velocity of the object from t = 1 s to t = 2 s. Find the position coordinate of the object's turning point after t = 0. At time t = 0, a particle in motion along the x-axis passes the position, x = 10 m, with a velocity that varies with time as: v(t) = 6 - 2t^2, where t is in seconds. Find the instantaneous velocity of the particle at the time, t = 3 s. Find the instantaneous acceleration of the particle at the time, t = 3 s. What is the average acceleration of the particle from t = 1 s to t = 3s? Calculate the average velocity of the object from t = 1 s to t = 3s. What is the magnitude of the acceleration of the particle when it reaches its turning point along the x-direction for time t > 0?Explanation / Answer
Here, displacement = t3/3 - 3/2t2 - 10t + 15
3) a) instantaneous velocity = t2 - 3t - 10
= 12 - 3 - 10 = - 12 m/s
b) average velocity = (- 8.33 - 3.833)/1
= - 12 m/s
c) position coordinate = (-15 -47)/2
= - 31 m
4) a) instantaneous velocity = 6 - 2 * 3 * 3
= - 12 m/s
b) instantaneous acceleration = - 4 * 3
= - 12 m/s2
c) average acceleration = (- 12 - 4)/2
= - 8 m/s2
d) average velocity = (10 - 15.33)/2
= - 2.67 m/s
e) magnitude of acceleration = -4 * 1.732 = - 6.93 m/s2
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