Question

use the graph below for all of the following questions...khari1. when is his acceleration negative?2. when is his acceleration positive?3. when is his acceleration zero?solve for the acceleration at each of the following time intervals:0s-3s 3s-7s 7s-10suse the graph below for all of the following questions...day-drion1. when is his acceleration negative?2. when is his acceleration positive?3. when is his acceleration zero?solve for the acceleration at each of the following time intervals:0s-4s 4s-6s 6s-10s

Explanation:

For Khari's Velocity-Time Graph

Step1: Recall acceleration formula

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

Step2: Calculate 0s-3s acceleration

$v_i=9\ \text{m/s}, v_f=9\ \text{m/s}, t_i=0, t_f=3$
$a = \frac{9-9}{3-0} = 0\ \text{m/s}^2$

Step3: Calculate 3s-7s acceleration

$v_i=9\ \text{m/s}, v_f=2\ \text{m/s}, t_i=3, t_f=7$
$a = \frac{2-9}{7-3} = \frac{-7}{4} = -1.75\ \text{m/s}^2$

Step4: Calculate 7s-10s acceleration

$v_i=2\ \text{m/s}, v_f=5\ \text{m/s}, t_i=7, t_f=10$
$a = \frac{5-2}{10-7} = \frac{3}{3} = 1\ \text{m/s}^2$

Step5: Identify negative acceleration interval

Negative acceleration when $a<0$: 3s to 7s

Step6: Identify positive acceleration interval

Positive acceleration when $a>0$: 7s to 10s

Step7: Identify zero acceleration interval

Zero acceleration when $a=0$: 0s to 3s

Step1: Recall acceleration formula

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

Step2: Calculate 0s-4s acceleration

$v_i=2\ \text{m/s}, v_f=8.5\ \text{m/s}, t_i=0, t_f=4$
$a = \frac{8.5-2}{4-0} = \frac{6.5}{4} = 1.625\ \text{m/s}^2$

Step3: Calculate 4s-6s acceleration

$v_i=8.5\ \text{m/s}, v_f=8.5\ \text{m/s}, t_i=4, t_f=6$
$a = \frac{8.5-8.5}{6-4} = 0\ \text{m/s}^2$

Step4: Calculate 6s-10s acceleration

$v_i=8.5\ \text{m/s}, v_f=5.5\ \text{m/s}, t_i=6, t_f=10$
$a = \frac{5.5-8.5}{10-6} = \frac{-3}{4} = -0.75\ \text{m/s}^2$

Step5: Identify negative acceleration interval

Negative acceleration when $a<0$: 6s to 10s

Step6: Identify positive acceleration interval

Positive acceleration when $a>0$: 0s to 4s

Step7: Identify zero acceleration interval

Zero acceleration when $a=0$: 4s to 6s

Answer:

1. Acceleration is negative: 3 s to 7 s
2. Acceleration is positive: 7 s to 10 s
3. Acceleration is zero: 0 s to 3 s
4. Acceleration values:

• 0s-3s: $0\ \text{m/s}^2$
• 3s-7s: $-1.75\ \text{m/s}^2$
• 7s-10s: $1\ \text{m/s}^2$

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For Day-Drion's Velocity-Time Graph