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.)