The position of the object at the following values of ( t ) : (a) 1 s , (b) 2 s , (c) 3 s – Free B1
The position of the object at the following values of ( t ) : (a) 1 s , (b) 2 s , (c) 3 s , and (d) 4 s . (e) What is the object’s displacement between ( t=0 ) and ( t=4 \mathrm{~s} ) ? (f) What is its average velocity from ( t=2 \mathrm{~s} ) to ( t=4 \mathrm{~s} ) ? Units Units Units Units Units Units
Answer
Motion of an Object Along the x-axis
The position of an object moving along the x-axis is given by the equation:
x(t) = 3.15t − 4.04t² + 1.09t³
where x is in meters (m) and t is in seconds (s).
(a) Position at t = 1 s
x(1) = 3.15 × 1 − 4.04 × 1² + 1.09 × 1³ = 3.15 − 4.04 + 1.09 = 0.2 m
Answer: 0.2 m
(b) Position at t = 2 s
x(2) = 3.15 × 2 − 4.04 × 4 + 1.09 × 8 = 6.30 − 16.16 + 8.72 = -1.14 m
Answer: -1.14 m
(c) Position at t = 3 s
x(3) = 3.15 × 3 − 4.04 × 9 + 1.09 × 27 = 9.45 − 36.36 + 29.43 = 2.52 m
Answer: 2.52 m
(d) Position at t = 4 s
x(4) = 3.15 × 4 − 4.04 × 16 + 1.09 × 64 = 12.6 − 64.64 + 69.76 = 17.72 m
Answer: 17.72 m
(e) Displacement between t = 0 s and t = 4 s
x(0) = 0
x(4) = 17.72
Displacement = x(4) − x(0) = 17.72 − 0 = 17.72 m
x(4) = 17.72
Displacement = x(4) − x(0) = 17.72 − 0 = 17.72 m
Displacement: 17.72 m
(f) Average Velocity from t = 2 s to t = 4 s
Average Velocity = (x(4) − x(2)) / (4 − 2) = (17.72 − (−1.14)) / 2 = 18.86 / 2 = 9.43 m/s
Average Velocity: 9.43 m/s
Summary of Answers
| Quantity | Value |
|---|---|
| Position at t = 1 s | 0.2 m |
| Position at t = 2 s | -1.14 m |
| Position at t = 3 s | 2.52 m |
| Position at t = 4 s | 17.72 m |
| Displacement (0 s to 4 s) | 17.72 m |
| Average Velocity (2 s to 4 s) | 9.43 m/s |