A particle starts from the origin at t=0 and moves along the positive x axis. – Free 3B
A particle starts from the origin at t=0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in the figure; the v-axis scale is set by vs=7.0ms. (a) What is the coordinate of the particle at t=5.0s ? (b) What is the velocity of the particle at t=5.0s ? (c) What is the acceleration of the particle at t=5.0s ? (d) What is the average velocity of the particle between t=1.0s and t=5.0s ? (e) What is the average acceleration of the particle between t=1.0s and t=5.0s ? (a) Number Units (b) Number I Units (c) Number Units (d) Number
Answer
Particle Motion Analysis Using Velocity-Time Graph
This step-by-step physics solution determines a particle’s position, velocity, acceleration, average velocity, and average acceleration based on a velocity-time graph.
Step 1: Velocity-Time Graph Overview
The velocity-time (VT) graph provides:
- Instantaneous velocity at specific times
- Displacement via area under the curve
- Acceleration from the slope
- Average velocity and average acceleration over intervals
Step 2: Position at t = 5.0 s
Calculate area under VT graph from 0 to 5 seconds:
x₂ = 2 × 7 = 14 m
x₃ = (½ × 1 × 3.5) + (1 × 3.5) = 5.25 m
x = 7 + 14 + 5.25 = 26.25 m
Step 3: Velocity at t = 5.0 s
Step 4: Acceleration at t = 5.0 s
Slope of line between t = 4 s and t = 6 s:
Step 5: Average Velocity from t = 1.0 s to t = 5.0 s
Time = 5.0 − 1.0 = 4.0 s
v_avg = 24.5 / 4.0 = 6.125 m/s
Step 6: Average Acceleration from t = 1.0 s to t = 5.0 s
Δt = 5 − 1 = 4 s
a_avg = 0 / 4 = 0 m/s²
Final Summary
| Parameter | Value |
|---|---|
| Position at t = 5.0 s | 26.25 m |
| Velocity at t = 5.0 s | 3.5 m/s |
| Acceleration at t = 5.0 s | −3.5 m/s² |
| Average velocity (1.0 s to 5.0 s) | 6.125 m/s |
| Average acceleration (1.0 s to 5.0 s) | 0 m/s² |