A car starts from rest and accelerates at a rate of 5.75 m/s/s for a time (t1) of 6.76 seconds. The car then maintains a constant speed for a time of 7.32 seconds (t2 minus t1). Finally, the car slows down at a rate of -4.21 m/s/s. Determine the total distance traveled by the car from its starting position to its stopping position.
I already got the first (131.38) and second (284.53) values for distance traveled, how can I get the third? I tried everything I could but nothing works.
you know the initial speed and the deceleration
with uniform deceleration, the average speed is half of the initial speed
time = initial speed / deceleration
distance = average speed * time
To determine the distance traveled during the third phase, you need to calculate the distance covered while the car is decelerating. Here's how you can find it:
1. Determine the final velocity (v_f) of the car at the end of the constant speed phase. To do this, multiply the constant speed (which is the same as the average speed during this phase) by the time it lasted:
v_f = constant speed x time during constant speed = 284.53 m/s
2. Now, you want to find the time (t3) it takes for the car to come to a stop during deceleration. The formula to calculate this is:
v_f = initial velocity + acceleration x time
Rearrange the formula to solve for time:
time during deceleration (t3) = (v_f - 0) / acceleration during deceleration
acceleration during deceleration = -4.21 m/s/s
t3 = (284.53 m/s - 0 m/s) / (-4.21 m/s/s) = -67.63 seconds
You may have noticed that this time is negative, which doesn't make sense. That's because the acceleration value (-4.21 m/s/s) should also be positive, indicating deceleration, not negative. Please review your values and ensure they are entered correctly.
Once you have the correct acceleration value during deceleration, you can proceed to the next step.
3. Calculate the distance traveled during deceleration using the formula:
distance during deceleration = initial velocity x time + 0.5 x acceleration x time^2
acceleration during deceleration = -4.21 m/s/s
time during deceleration = t3 (make sure it is positive)
initial velocity = v_f (from step 1)
Plug in the values and calculate:
distance during deceleration = v_f x t3 + 0.5 x acceleration during deceleration x t3^2
Using these steps, you should be able to find the distance traveled during deceleration.