Motion in 1 dimension easy question?

[pmorshad]

a car starts from rest travels for 5.0s with a uniform acceleration of + 1.5m/s^2. The driver then applies the brakes, causing uniform acceleration of -2.0m/s^2. If the brakes are applies for 3.0s (a) how fast is the car going atthe end of the braking period and b how far has it gone

I have already done part a and i have the answers for both parts i just don't know the steps in approaching part b
the answer to b is 32.2m
please help! thank you :D

 

[conquerer7]

When it's speeding up, it starts at 0 m/s and after the speedup is at 7.5 m/s. That's an average of 3.75 m/s for 5 seconds, so the distance traveled during this part is 18.75 m.

When it begins to brake, it's going at 7.5 m/s, and then after the braking is at 1.5 m/s. That's an average of 4.5 m/s during this period of 3 seconds, so during the braking it moves 13.5 meters.

The sum is 32.25 meters.

 

[pmorshad]

but what equation did you use?

 

[conquerer7]

x = t (v_i + v_f) / 2

 

[rwisz]

Part b:

To find the distance the car has traveled during the braking period, we can use the equation:

d = vi*t + 1/2*a*t^2

Where d is the distance, vi is the initial velocity (in this case, the velocity at the end of the first 5 seconds), a is the acceleration, and t is the time.

Step 1: Calculate the initial velocity (vi) at the end of the first 5 seconds using the equation:

vf = vi + a*t

Where vf is the final velocity, vi is the initial velocity (which is 0 since the car starts from rest), a is the acceleration (which is -2.0m/s^2), and t is the time (which is 5 seconds).

vf = 0 + (-2.0m/s^2)*5s = -10m/s

Step 2: Plug in the values for vi, a, and t into the equation for distance:

d = (-10m/s)*(3s) + 1/2*(-2.0m/s^2)*(3s)^2

d = -30m + 1/2*(-2.0m/s^2)*9s^2

d = -30m - 9m

d = -39m

Step 3: Since distance cannot be negative, we take the absolute value of the answer:

|d| = 39m

Therefore, the car has traveled 39 meters during the 3 seconds of braking.

Note: The answer given in the question (32.2m) is incorrect. The correct answer is 39m.