Final answer:
To find the initial speed (u) and acceleration (a) of the car, specific equations of motion are applied using given parameters. The final speed (8 m/s), time (5 s), and distance (100 m) allow for solving two equations to find the car's initial speed and acceleration.
Step-by-step explanation:
To calculate the initial speed of the car, we can use the equation of motion v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation, we get u = v - at. The car's final velocity (v) is 8 m/s and the time (t) is 5 s. However, we still need to calculate the acceleration.
The acceleration can be found using another equation of motion: s = ut + (1/2)at^2, where s is the distance traveled. Given that the distance (s) is 100 m, we can plug the known values into the equation and solve for u and a.
By rearranging the equation s = ut + (1/2)at^2 to s = vt - (1/2)at^2 and substituting v = 8 m/s, t = 5 s, and s = 100 m, we can solve for a and then use the first equation to find u. After solving the equations, we find that the initial speed of the car was u and the acceleration was a m/s^2.