Answer:
See attachment
1512 ft
Explanation:
Since the acceleration is either constant or zero, the a−t curve is made of horizontal straight-line segments. The values of t2 and a4 are determined as follows:
Acceleration - Time
0 < t < 6: Change in v = area under a–t curve
V_6 - 0 = (6 s)(4 ft/s2
) = 24 ft/s
6 < t < t2: Since the velocity increases from 24 to 48 ft/s,
Change in v = area under a–t curve
48 - 24 = (t2 - 6) * 6
t2 = 10 s
t2 < t < 34: Since the velocity is constant, the acceleration is zero.
34 < t < 40: Change in v = area under a–t curve
0 - 42 = 6*a4
a4 = - 8 ft / s^2
The acceleration being negative, the corresponding area is below the t axis; this area represents a decrease in velocity.
Velocity - Time
Since the acceleration is either constant or zero, the v−t curve is made of straight-line segments connecting the points determined above.
Change in x = area under v−t curve
0 < t < 6: x6 - 0 = 0.5*6*24 = 72 ft
6 < t < 10: x10 - x6 = 0.5*4*(24 + 48) = 144 ft
10 < t < 34: x34 - x10 = 48*24 = 1152 ft
34 < t < 40: x40 - x34 = 0.5*6*48 = 144 ft
Adding the changes in x, we obtain the distance from A to B:
d = x40 - 0 = 1512 ft
