A car starts from rest and accelerates at 5m/s^2 for 4s, then maintains that velocity for 3 seconds and then decelerates to a rate of 2m/s^2 for 3 seconds. How far does the car travel?
I would have to add the total distance throughout the trip. And to find the distance I would use:
d= d_0 + v_0t + 1/2at^2
=0+ 0(4) +1/2(5)(4^2) = 40m
=40+ 0(3) +1/2(5)(3^2) = 62.5m
=62.5 + 0(3) +1/2(2)(3^2)= 71.5m
thus 40 + 62.5 + 71.5 = 174m
On the second period, acceleration is zero (it maintains velocity as a constant). D during the second period is velocity*time=20*3=60
Now during the final period,
d=vi*t+1/2 at^2=20*3-1/2 2*9=42m check that.
The total distance is the sum of distances...
40+60+42.
Now a word on your work. YOu got the second and third wrong, (see above), however, you use of the formula bothers me...
df=do + vi*t + 1/2 a t^2. do is the the distance already traveled if you use this formula. Then, the prior distances are already added, you do not add them again as you did.
To find the distance traveled by the car, you need to calculate the distance covered during each phase of its motion and then add them up.
First, let's calculate the distance covered during the acceleration phase. We can use the formula:
d = d_0 + v_0t + 1/2at^2
where:
d = distance covered
d_0 = initial displacement (in this case, 0 since the car starts from rest)
v_0 = initial velocity (in this case, 0 since the car starts from rest)
t = time (4 seconds in this case)
a = acceleration (5 m/s^2 in this case)
Using these values, we can calculate the distance covered during the acceleration phase:
d1 = 0 + 0(4) + 1/2(5)(4^2)
= 0 + 0 + 1/2(5)(16)
= 0 + 0 + 40
= 40 meters
Next, let's calculate the distance covered during the constant velocity phase. The car maintains a velocity for 3 seconds, so we can use the formula:
d2 = v*t
where:
d2 = distance covered during the constant velocity phase
v = velocity during this phase (which is the same as the final velocity reached during the acceleration phase, in this case 20 m/s)
t = time during this phase (3 seconds)
Using these values, we can calculate the distance covered during the constant velocity phase:
d2 = 20 * 3
= 60 meters
Lastly, let's calculate the distance covered during the deceleration phase. We will use the same formula as before:
d3 = d_0 + v_0t + 1/2at^2
where:
d3 = distance covered during the deceleration phase
d_0 = initial displacement (in this case, the distance covered during the previous phases, which is 40 + 60 = 100 meters)
v_0 = initial velocity (which is the final velocity reached during the constant velocity phase, in this case 20 m/s)
t = time (3 seconds)
a = deceleration (2 m/s^2 in this case)
Using these values, we can calculate the distance covered during the deceleration phase:
d3 = 100 + 20(3) + 1/2(2)(3^2)
= 100 + 60 + 1/2(2)(9)
= 100 + 60 + 1/2(18)
= 100 + 60 + 9
= 169 meters
Finally, to find the total distance traveled by the car, we add up the distances covered during each phase:
total distance = d1 + d2 + d3
= 40 + 60 + 169
= 269 meters