A car drives north. At t=0, it passes a road sign. The distance north of the sig

Question

A car drives north. At t=0, it passes a road sign. The distance north of the sign is given by y = 2t + 5t^-1 a. Find the expression for the car's instantaneous velocity as a function of time. b. Find the expression for the car's acceleration as function of time. Does the car experience constant acceleration? c. find the average velocity between t=1s and t=3s. d. What is the car's instantaneous velocity at t=1s? e. What is the cars instantaneous velocity and acceleration at t=3s? A motor cyclist has constant acceleration of 4 m/s^2. At t=0, he is 5m east of a road sign and is traveling east at 15 m/s. a. We want to find his position a t=2.0 s. First, choose an origin for your coordinate system, and identify the initial and final states. Also write down the initial and final quantities. b. Choose a constant acceleration equation which includes your desired quantity as the only unknown (if possible). In this case the unknown is the position at t=2s, for this position. c. Follow the same procedures to find the velocity at t = 2s. d. Follow the same procedures to find the position when the motorcycle has a velocity of 25 m/s A car traveling at 15 m/s passes a police car. At that instant, the police car accelerates at a constant rate of 3 m/s^2 in pursuit. We wish to find how much time elapses before the officer catches the car. a. Choose a coordinate system for this problem and identify the initial states starting when the car passes the police. b. Define the final state or conditions which enables you to answer the above question.

Explanation / Answer

3)   Distance = y = 2t + 5t^-1

a) Instantaneous velocity = v(t) = dy/dt = 2 – 5t^-2

b) Acceleration = a(t) = dv(t)/dt = 10t^-3 (The acceleration is not constant)

c) v(1) = -3      and     v(3) = 1.44

Average velocity = -0.78 m/s

d) Instantaneous velocity at t = 1s ======> -3 m/s

e) Instantaneous velocity at t = 3s ======> 1.44 m/s

     and acceleration = 0.37 m/s^2

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