1. Suppose that a particle moves along a straight line with acceleration a(t) =-6t+2 meters per...

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1. Suppose that a particle moves along a straight line with acceleration a(t) =-6t+2 meters per second per second at time t seconds. Suppose that we fix the positive direction as motion to the right, and that at time t = 0 seconds, the object is 2 meters to the left of the reference point and is moving to the right at 3 meters per second. (a) (4 points) Let s(t) be the object's position in meters at time t seconds. Write down a second order differential equation for s(t) and two initial values expressing the above information. Give units. (b) (6 points) Solve your differential equation. (c) (4 points) How many times does the particle pass the reference points? And if the particle does pass the reference point, at what time(s)? (d) (4 points) Does the particle ever turn around? If so, at what time? 1. Suppose that a particle moves along a straight line with acceleration a(t) =-6t+2 meters per second per second at time t seconds. Suppose that we fix the positive direction as motion to the right, and that at time t = 0 seconds, the object is 2 meters to the left of the reference point and is moving to the right at 3 meters per second. (a) (4 points) Let s(t) be the object's position in meters at time t seconds. Write down a second order differential equation for s(t) and two initial values expressing the above information. Give units. (b) (6 points) Solve your differential equation. (c) (4 points) How many times does the particle pass the reference points? And if the particle does pass the reference point, at what time(s)? (d) (4 points) Does the particle ever turn around? If so, at what time?

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a Second Order Differential Equation for st The acceleration at is the second derivative of the posi... View the full answer