Question

The figure shows the velocity of an object moving along a straight line as a function of time. Determine: 

a) The displacement of the object for the first 9 seconds

b) The object's average velocity from t = 0 s tot=9 s.

c) The object's average acceleration from t = 0 tot = 5 seconds.

c) The acceleration of the object at t =8 seconds.

Answer 1

Answer 2

SOLUTION :

a.

Displacement in 9 secs. :

                                                          9

= Net area ( since displacement = ∫ t f(t)) dt )

                                                          0

= 1/2 * 8 * 4 - 1/2 * 1 * 1

= 16 -  1/2

= 15.5 m (ANSWER)

b.

Average velocity 

= Total displacement / time duration 

= 15.5 / 9

= 1.72 m/s (ANSWER)

c.

Average acceleration  (0-5 sec) = 3 / 5 = 0.6 m/sec^2 (ANSWER).

d.

Acceleration at (t = 8 sec) = – 4 / 4 = - 1 m/sec^2 (ANSWER).