To calculate the force needed to produce this acceleration, we'll first need to find the acceleration of the vehicle and then apply Newton's second law of motion, which states that force is equal to mass times acceleration (F = m * a).
Step 1: Find the Acceleration
Acceleration (a) can be calculated using the formula:
\[ a = \frac{\Delta v}{t} \]
where:
\( \Delta v \) = change in velocity (final velocity - initial velocity)
\( t \) = time taken for this change in velocity
Since the vehicle starts from rest, the initial velocity (v_i) is 0 m/s. The final velocity (v_f) given is 8.0 m/s, and the time (t) taken to reach this velocity is 20 seconds.
Therefore, the acceleration \( a \) is:
\[ a = \frac{v_f - v_i}{t} \]
\[ a = \frac{8.0 \, \text{m/s} - 0 \, \text{m/s}}{20 \, \text{s}} \]
\[ a = \frac{8.0 \, \text{m/s}}{20 \, \text{s}} \]
\[ a = 0.4 \, \text{m/s}^2 \]
Step 2: Calculate the Force
Once we have the acceleration, we can calculate the force (F) with Newton's second law:
\[ F = m \times a \]
Given the mass (m) of the vehicle is 600 kg and the acceleration (a) we found is 0.4 m/s^2, the force is:
\[ F = 600 \, \text{kg} \times 0.4 \, \text{m/s}^2 \]
\[ F = 240 \, \text{N} \]
The force needed to produce this acceleration is 240 Newtons.
