5.4 Integration & Anti-derivatives
Question #4 (Medium): Working With Acceleration, Velocity, Displacement, and Distance
Acceleration is the derivative of velocity. Velocity is the derivative of displacement.
Thus, ( ) ( ) , and ( ) ( ) .
Displacement is the net distance travelled, so ∫ ( ) .
But Distance is the total distance travelled, so ∫ | ( )| .
The given acceleration (in ) and the initial velocity (in ) describe a particle moving along a line.
( ) , ( ) ,
1) Find the velocity at time .
2) Find the total distance travelled during the given time interval.
1) Velocity is the anti-derivative of acceleration:
Thus, ( ) ∫ ( ) ∫ ( )
a. Since ( ) , then ( ) ( ) . So the constant factor
So the velocity function at