Two points on a velocity time-graph have coordinates (5 s, 10 ms-1) and (20 s, 20 -1). Calculate the mean acceleration between the two points
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Let's calculate the mean acceleration.
Step 1: Identify the given coordinates.
Point 1: $(t_1, v_1) = (5 \text{ s}, 10 \text{ m/s})$
Point 2: $(t_2, v_2) = (20 \text{ s}, 20 \text{ m/s})$
Step 2: Use the formula for mean acceleration.
Mean acceleration ($a$) is the change in velocity ($\Delta v$) divided by the change in time ($\Delta t$):
$$a = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{t_2 - t_1}$$
Step 3: Substitute the values into the formula.
$$a = \frac{20 \text{ m/s} - 10 \text{ m/s}}{20 \text{ s} - 5 \text{ s}}$$
Step 4: Calculate the mean acceleration.
$$a = \frac{10 \text{ m/s}}{15 \text{ s}}$$
$$a = \frac{2}{3} \text{ m/s}^2$$
$$a \approx 0.667 \text{ m/s}^2$$
The mean acceleration between the two points is $\boxed{\text{0.667 m/s}^2}$.
