Question

the acceleration must be calculated from the change in velocity, not the absolute value.
to find the acceleration between 6 s and 10 s:
initial velocity =
final velocity =
$delta t$ =
$a=\frac{vf - vi}{t} = $
$a=$

Explanation:

Step1: Identify initial velocity

From the graph, at \(t=6\ \text{s}\), initial velocity \(v_i = 5\ \text{m/s}\)

Step2: Identify final velocity

From the graph, at \(t=10\ \text{s}\), final velocity \(v_f = 2\ \text{m/s}\)

Step3: Calculate time interval

Find \(\Delta t = t_f - t_i\)
\(\Delta t = 10 - 6 = 4\ \text{s}\)

Step4: Substitute into acceleration formula

Use \(a=\frac{v_f - v_i}{\Delta t}\)
\(a=\frac{2 - 5}{4}\)

Step5: Compute acceleration

Simplify the expression
\(a=\frac{-3}{4} = -0.75\ \text{m/s}^2\)

Answer:

initial velocity = \(5\ \text{m/s}\)
final velocity = \(2\ \text{m/s}\)
\(\Delta t = 4\ \text{s}\)
\(a=\frac{2-5}{4}\)
\(a = -0.75\ \text{m/s}^2\)