The car moving along a straight road is a problem in one-dimensional motion, and

Question

The car moving along a straight road is a problem in one-dimensional motion, and the question calls for using the relation between position and time to calculate speed and velocity.

ANALYZE (A) Determine how the velocity varies for positive acceleration and initial velocity to the right.

The acceleration vs. time plot for constant acceleration is a straight line parallel to the time axis. It lies above the origin for acceleration to the right. During the acceleration, the velocity increases by 1.3 m/s each second, so the velocity vs. time graph is a line with a slope of 1.3 m/s per second, and

v(t) = vi + at = (_______m/s) + (________m/s2) t.

he car starts moving to the right and its speed to the right simply continues to increase.

(B) Determine how the velocity varies for velocity initially to the right and with constant acceleration to the left. In this case the velocity is initially positive but its value decreases by 1.3 m/s for each second that passes. Because the acceleration is to the left, it is negative. The velocity vs. time graph satisfies the equation

v(t) = vi + at = (______m/s) +(______ m/s2) t.

The car moves initially to the right and while it moves its velocity keeps decreasing. Eventually, its velocity passes through zero and thereafter the car is backing up with increasing speed. FINALIZE Check whether this description of motion is consistent with the graphs shown in the Active Figure and the motion it illustrates. Deceleration is an acceleration that causes an object to slow down. Would it be consistent with our sign conventions to define deceleration instead as "negative acceleration?"

Yes or No???

Explanation / Answer

a)

velocity at any time for object with positive acceleration is given as

Vf = Vi + at

V(t) = Vi + 1.3 t

B)

V(t) = Vi - 1.3 t

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