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Name Period Date Energy: Worksheet 5 Indefinite Integrals with Particular Solutions For questions 1 – 2, determine the velocity function for each acceleration function and initial condition. m 1. a 3t 2 1 when v (1s ) 4 s m m m 2. a (t ) (2 5 )t 3 (4 4 )t 2 when v (0s ) 0 s s s 3. Determine the position at t 2s for an object whose acceleration is given by m and x (0 s ) 1m . a (t ) 6t 2 4 if v (0s ) 2 s Energy: Worksheet 5 page 2 4. An object rolling down an incline has an acceleration of 0.80 g . If it starts from rest, how far will it have rolled after 2.0 s? 5. The velocity of a particle is given by v (t ) 8.0t 3 6.0t 2 2.0 . If x (0) 0m , what is the particle’s position and acceleration at t 2.0s ? 6. The net force on a 10. kg object is given by F (t ) 2.0t 1.0 . If it starts from rest, what are its velocity at t 5.0s and its displacement from t 2.0s to t 5.0s ? (Hint: Think of Newton’s Second Law.)