To solve this problem, we'll use fundamental equations from kinematics and Newton's second law.
First, we will calculate the acceleration (a) the car experienced. Acceleration is defined as the change in velocity (Δv) over the change in time (Δt).
The change in velocity (Δv) is the final velocity (v_f) minus the initial velocity (v_i):
Δv = v_f - v_i
The final velocity (v_f) is 60 m/s, and the initial velocity (v_i) is 40 m/s. The change in time (Δt) is 10 seconds.
So, acceleration (a) can be calculated as:
a = Δv / Δt
a = (60 m/s - 40 m/s) / 10 s
a = 20 m/s / 10 s
a = 2 m/s²
Now, with the acceleration known, we can calculate the distance (d) traveled during this time. One of the kinematic equations relates distance, initial velocity, time, and acceleration:
d = v_i t + 0.5 a t²
Here, t is the time during which the velocity change occurred, which is 10 seconds.
Plugging in the values:
d = 40 m/s 10 s + 0.5 2 m/s² (10 s)²
d = 400 m + 0.5 2 m/s² 100 s²
d = 400 m + 1 m/s² 100 s²
d = 400 m + 100 m
d = 500 m
Lastly, we'll calculate the force applied using Newton's second law, which states that force (F) equals mass (m) multiplied by acceleration (a):
F = m a
The mass of the car (m) is given as 500 kg, and we've calculated the acceleration (a) as 2 m/s².
So:
F = 500 kg * 2 m/s²
F = 1000 N
Therefore, the car experienced an acceleration of 2 m/s², traveled a distance of 500 meters, and had 1000 Newtons of force applied to it over the 10-second period.
