Question

date: class # 2velocity vs. time graphsexpert levelhelicopter flight1. when is the acceleration negative?2. when is the acceleration positive?3. when is the acceleration zero?what is the helicopters velocity at 2 seconds?what is the helicopters velocity at 6 seconds?what is the helicopters velocity at 8 seconds?what is the helicopters velocity at 10 seconds?solve for the acceleration during each of the following time intervals:0s-4s 4s-6s 6s-8s 8s-10s

Explanation:

Step1: Analyze acceleration sign rules

Acceleration is the slope of velocity-time graph:

• Negative slope = negative acceleration
• Positive slope = positive acceleration
• Zero slope = zero acceleration

Step2: Identify velocity at given times

Read directly from the graph:

• At t=2s: $v=5\ \text{m/s}$
• At t=6s: $v=1.5\ \text{m/s}$
• At t=8s: $v=1.5\ \text{m/s}$
• At t=10s: $v=5.5\ \text{m/s}$

Step3: Calculate acceleration for intervals

Acceleration formula: $a=\frac{\Delta v}{\Delta t}=\frac{v_f - v_i}{t_f - t_i}$

Interval 0s-4s:

$a=\frac{7-3}{4-0}=\frac{4}{4}=1\ \text{m/s}^2$

Interval 4s-6s:

$a=\frac{1.5-7}{6-4}=\frac{-5.5}{2}=-2.75\ \text{m/s}^2$

Interval 6s-8s:

$a=\frac{1.5-1.5}{8-6}=\frac{0}{2}=0\ \text{m/s}^2$

Interval 8s-10s:

$a=\frac{5.5-1.5}{10-8}=\frac{4}{2}=2\ \text{m/s}^2$

Step4: Match slope to acceleration sign

• Negative slope: 4s to 6s
• Positive slope: 0s to 4s, 8s to 10s
• Zero slope: 6s to 8s

Answer:

1. Acceleration is negative: 4 seconds to 6 seconds
2. Acceleration is positive: 0 seconds to 4 seconds, 8 seconds to 10 seconds
3. Acceleration is zero: 6 seconds to 8 seconds
4. Velocity at 2 seconds: $5\ \text{m/s}$
5. Velocity at 6 seconds: $1.5\ \text{m/s}$
6. Velocity at 8 seconds: $1.5\ \text{m/s}$
7. Velocity at 10 seconds: $5.5\ \text{m/s}$
8. Acceleration for intervals:

• 0s-4s: $1\ \text{m/s}^2$
• 4s-6s: $-2.75\ \text{m/s}^2$
• 6s-8s: $0\ \text{m/s}^2$
• 8s-10s: $2\ \text{m/s}^2$